Metrics for x / (x^2 + 1)

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 9 to 6 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

ival-div: 0.0ms (0% of total)

ival-add: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample536.0ms (12.9%)

Results

359.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 197.0ms

ival-mult: 77.0ms (39% of total)

ival-div: 58.0ms (29.4% of total)

ival-add: 49.0ms (24.8% of total)

const: 10.0ms (5.1% of total)

backward-pass: 3.0ms (1.5% of total)

Bogosity

preprocess29.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

280×	`fnmadd-define`
254×	`sum3-define`
246×	`fma-define`
144×	`fmsub-define`
134×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	30	19
2	68	18
3	146	18
4	304	18
5	549	18
6	872	18
7	874	18
8	898	18
9	914	18
0	5	6
1	9	6
0	9	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ x (+ (* x x) 1))

Outputs
(/ x (+ (* x x) 1))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Call 2

Inputs
(/ x (+ (* x x) 1))
(/ (neg x) (+ (* (neg x) (neg x)) 1))
(neg (/ (neg x) (+ (* (neg x) (neg x)) 1)))

Outputs
(/ x (+ (* x x) 1))
(/ x (fmsub x x -1))
(/ (neg x) (+ (* (neg x) (neg x)) 1))
(/ x (fnmsub x x 1))
(neg (/ (neg x) (+ (* (neg x) (neg x)) 1)))
(/ x (fmsub x x -1))

Symmetry

(negabs x)

explain66.0ms (1.6%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
63	-	-	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
0	-	-	`x`
0	-	-	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`#s(literal 1 binary64)`

Results

27.0ms

512×

valid

Compiler

Compiled 46 to 17 computations (63% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 5.0ms (42.4% of total)

ival-div: 4.0ms (33.9% of total)

ival-add: 3.0ms (25.5% of total)

const: 1.0ms (8.5% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 8 to 5 computations (37.5% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.9%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	cost-diff	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`fma-lowering-fma.f32`
2×	`fma-define`
2×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
1	9	15
0	9	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x (+ (* x x) 1))
x
(+ (* x x) 1)
(* x x)
1

Outputs
(/ x (+ (* x x) 1))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
x
(+ (* x x) 1)
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(* x x)
(*.f64 x x)
1
#s(literal 1 binary64)

localize20.0ms (0.5%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	accuracy	76.9%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

14.0ms

256×

valid

Compiler

Compiled 19 to 6 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-div: 2.0ms (33.9% of total)

ival-mult: 2.0ms (33.9% of total)

ival-add: 1.0ms (16.9% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series2.0ms (0%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (/ x (+ (* x x) 1))>
#<alt (+ (* x x) 1)>
#<alt (* x x)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/ x (+ (* x x) 1))
0.0ms	x	@	-inf	(/ x (+ (* x x) 1))
0.0ms	x	@	0	(/ x (+ (* x x) 1))
0.0ms	x	@	inf	(+ (* x x) 1)
0.0ms	x	@	inf	(* x x)

rewrite297.0ms (7.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3352×	`/-lowering-/.f32`
3352×	`/-lowering-/.f64`
2528×	`-lowering-.f32`
2528×	`-lowering-.f64`
1738×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	31	13
2	207	13
3	1921	13
0	8610	13

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 322

Calls

Call 1

Inputs
(/ x (+ (* x x) 1))
(+ (* x x) 1)
(* x x)

Outputs
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (.f64 x x)) (.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(+.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(+.f64 (.f64 (.f64 x x) (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))) (.f64 #s(literal -1 binary64) (/.f64 x (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(exp.f64 (+.f64 (log.f64 x) (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64)) (log.f64 x)))
(-.f64 #s(literal 0 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal 1 binary64))) (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x))))
(-.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x)))
(fma.f64 (.f64 x x) (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (.f64 #s(literal -1 binary64) (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))))
(fma.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x))) (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(fma.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (.f64 x x) (.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x)))))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x x)) x))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))))))
(/.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 x (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (.f64 x x)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (*.f64 x x))))
(/.f64 (.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (.f64 x (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))))) (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (/.f64 x #s(literal 1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal -1 binary64) (.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x x)))
(/.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (.f64 x x)))) (+.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (.f64 x x)))
(/.f64 (.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (+.f64 (.f64 x x) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1 binary64)))))
(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) x)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) x)) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x x)) x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 x (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 x #s(literal -1 binary64)))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))))
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(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (+.f64 (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (.f64 x x)))) (+.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (.f64 x x)))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64)))))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64)))))))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))

simplify245.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

2026×	`sum4-define`
1714×	`sum3-define`
1512×	`-lowering-.f32`
1512×	`-lowering-.f64`
1410×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	211
1	137	195
2	355	185
3	1067	182
4	3300	182
0	8302	182

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x x))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(+.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(+.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval41.0ms (1%)

Compiler: Compiled 11877 to 1046 computations (91.2% saved)

prune161.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	353	5	358
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	353	6	359

Accuracy

100.0%

Counts

359 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.4%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
✓	76.9%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
▶	76.8%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) x))
▶	47.8%	(/.f64 #s(literal 1 binary64) x)
▶	53.3%	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
▶	53.8%	x

Compiler

Compiled 76 to 49 computations (35.5% saved)

simplify131.0ms (3.2%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) (*.f64 x x))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 x x))
✓	cost-diff	0	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	cost-diff	128	(/.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) x))

Rules

1486×	`fnmadd-define`
1276×	`sum5-define`
1204×	`--lowering--.f32`
1204×	`--lowering--.f64`
1112×	`sum3-define`

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	13	71
1	30	71
2	45	68
3	74	67
4	152	67
5	255	67
6	415	67
7	961	67
8	3932	67
9	6575	64
0	8205	64

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (/ (+ (* x x) 1) x))
1
(/ (+ (* x x) 1) x)
(+ (* x x) 1)
(* x x)
x
x
(/ 1 x)
1
x
(* x (- 1 (* x x)))
x
(- 1 (* x x))
1
(* x x)
(/ (+ 1 (/ -1 (* x x))) x)
(+ 1 (/ -1 (* x x)))
1
(/ -1 (* x x))
-1
(* x x)
x

Outputs
(/ 1 (/ (+ (* x x) 1) x))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
1
#s(literal 1 binary64)
(/ (+ (* x x) 1) x)
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(+ (* x x) 1)
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* x x)
(*.f64 x x)
x
x
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(* x (- 1 (* x x)))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
x
(- 1 (* x x))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
1
#s(literal 1 binary64)
(* x x)
(*.f64 x x)
(/ (+ 1 (/ -1 (* x x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(+ 1 (/ -1 (* x x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
1
#s(literal 1 binary64)
(/ -1 (* x x))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
-1
#s(literal -1 binary64)
(* x x)
(*.f64 x x)
x

localize62.0ms (1.5%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
✓	accuracy	99.9%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
✓	accuracy	99.4%	(/.f64 #s(literal -1 binary64) (*.f64 x x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	99.9%	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) x))
✓	accuracy	76.9%	(/.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) x)

Results

38.0ms

256×

valid

Compiler

Compiled 78 to 14 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-div: 10.0ms (53% of total)

ival-mult: 4.0ms (21.2% of total)

ival-add: 3.0ms (15.9% of total)

ival-sub: 1.0ms (5.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series5.0ms (0.1%)

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (/ 1 (/ (+ (* x x) 1) x))>
#<alt (/ (+ (* x x) 1) x)>
#<alt (+ (* x x) 1)>
#<alt (* x x)>
#<alt (/ 1 x)>
#<alt (* x (- 1 (* x x)))>
#<alt (- 1 (* x x))>
#<alt (/ (+ 1 (/ -1 (* x x))) x)>
#<alt (+ 1 (/ -1 (* x x)))>
#<alt (/ -1 (* x x))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt x>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* -1 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (/ -1 (pow x 3))>
#<alt (/ (- (pow x 2) 1) (pow x 3))>
#<alt (/ (- (pow x 2) 1) (pow x 3))>
#<alt (/ (- (pow x 2) 1) (pow x 3))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (/ -1 (pow x 2))>
#<alt (/ (- (pow x 2) 1) (pow x 2))>
#<alt (/ (- (pow x 2) 1) (pow x 2))>
#<alt (/ (- (pow x 2) 1) (pow x 2))>
#<alt 1>
#<alt (- 1 (/ 1 (pow x 2)))>
#<alt (- 1 (/ 1 (pow x 2)))>
#<alt (- 1 (/ 1 (pow x 2)))>
#<alt 1>
#<alt (- 1 (/ 1 (pow x 2)))>
#<alt (- 1 (/ 1 (pow x 2)))>
#<alt (- 1 (/ 1 (pow x 2)))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/ -1 (* x x))
0.0ms	x	@	inf	(/ (+ (* x x) 1) x)
0.0ms	x	@	-inf	(/ 1 x)
0.0ms	x	@	0	(* x (- 1 (* x x)))
0.0ms	x	@	inf	(* x (- 1 (* x x)))

rewrite253.0ms (6.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3166×	`-lowering-.f32`
3166×	`-lowering-.f64`
3044×	`/-lowering-/.f32`
3044×	`/-lowering-/.f64`
1070×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	91	51
2	719	47
0	8815	47

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 620

Calls

Call 1

Inputs
(/ 1 (/ (+ (* x x) 1) x))
(/ (+ (* x x) 1) x)
(+ (* x x) 1)
(* x x)
(/ 1 x)
(* x (- 1 (* x x)))
(- 1 (* x x))
(/ (+ 1 (/ -1 (* x x))) x)
(+ 1 (/ -1 (* x x)))
(/ -1 (* x x))

Outputs
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x x)) (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(+.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(+.f64 (.f64 (.f64 x x) (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 #s(literal -1 binary64) (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(exp.f64 (.f64 #s(literal -1 binary64) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) x))))
(-.f64 #s(literal 0 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x))))
(neg.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x x)) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 x x))))
(/.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))))))
(/.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))))))))
(/.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 1 binary64)))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))))))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x) #s(literal -1 binary64))
(pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x))))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 x x))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64))
(.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) x)
(.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal -1 binary64))
(.f64 (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 x x))) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64)))))
(.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64)))))))
(.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) #s(literal 1 binary64)))
(.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))) #s(literal 1 binary64)))
(.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (*.f64 x x) #s(literal -1 binary64)))
(.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))))
(.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)) x)
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) x)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64))) (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 x x) #s(literal -1 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal -1 binary64)) x)
(.f64 (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))) (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(literal -1 binary64)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) x))
(.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
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(exp.f64 (.f64 (log.f64 (.f64 x (-.f64 #s(literal 0 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
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(/.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 0 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x))
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(/.f64 (/.f64 #s(literal -1 binary64) x) x)
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)
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(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
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(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) x))
(.f64 (pow.f64 (.f64 x (-.f64 #s(literal 0 binary64) x)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x (-.f64 #s(literal 0 binary64) x)) #s(literal -1/2 binary64)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))

simplify196.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

2236×	`-lowering-.f32`
2236×	`-lowering-.f64`
1776×	`fnmsub-define`
1676×	`/-lowering-/.f32`
1676×	`/-lowering-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	675
1	170	574
2	452	541
3	1623	538
4	6118	538
0	8107	538

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/ 1 x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* -1 (pow x 2))))
(* -1 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 3))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(/ -1 (pow x 3))
(/ (- (pow x 2) 1) (pow x 3))
(/ (- (pow x 2) 1) (pow x 3))
(/ (- (pow x 2) 1) (pow x 3))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/ -1 (pow x 2))
(/ (- (pow x 2) 1) (pow x 2))
(/ (- (pow x 2) 1) (pow x 2))
(/ (- (pow x 2) 1) (pow x 2))
1
(- 1 (/ 1 (pow x 2)))
(- 1 (/ 1 (pow x 2)))
(- 1 (/ 1 (pow x 2)))
1
(- 1 (/ 1 (pow x 2)))
(- 1 (/ 1 (pow x 2)))
(- 1 (/ 1 (pow x 2)))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x x))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 x (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (pow x 2)) x)
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(/ (+ 1 (pow x 2)) x)
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(/ (+ 1 (pow x 2)) x)
(+.f64 x (/.f64 #s(literal 1 binary64) x))
x
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
x
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(/ -1 (pow x 3))
(/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))
(/ (- (pow x 2) 1) (pow x 3))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (pow x 2) 1) (pow x 3))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (pow x 2) 1) (pow x 3))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ (- (pow x 2) 1) (pow x 2))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/ (- (pow x 2) 1) (pow x 2))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/ (- (pow x 2) 1) (pow x 2))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
1
#s(literal 1 binary64)
(- 1 (/ 1 (pow x 2)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(- 1 (/ 1 (pow x 2)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(- 1 (/ 1 (pow x 2)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
1
#s(literal 1 binary64)
(- 1 (/ 1 (pow x 2)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(- 1 (/ 1 (pow x 2)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(- 1 (/ 1 (pow x 2)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))

eval302.0ms (7.3%)

Compiler: Compiled 17340 to 1783 computations (89.7% saved)

prune82.0ms (2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	799	1	800
Fresh	0	0	0
Picked	2	3	5
Done	0	1	1
Total	801	5	806

Accuracy

100.0%

Counts

806 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.9%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
▶	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	47.8%	(/.f64 #s(literal 1 binary64) x)
✓	53.3%	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
✓	53.8%	x

Compiler

Compiled 30 to 19 computations (36.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	(+.f64 x (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))

Rules

4×	`+-lowering-+.f64`
4×	`/-lowering-/.f32`
4×	`/-lowering-/.f64`
4×	`+-lowering-+.f32`
4×	`add-recip`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	10	13
0	10	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ 1 (+ x (/ 1 x)))
1
(+ x (/ 1 x))
x
(/ 1 x)

Outputs
(/ 1 (+ x (/ 1 x)))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
1
#s(literal 1 binary64)
(+ x (/ 1 x))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
x
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)

localize22.0ms (0.5%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(+.f64 x (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))

Results

13.0ms

256×

valid

Compiler

Compiled 19 to 6 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-div: 4.0ms (72% of total)

ival-add: 1.0ms (18% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (/ 1 (+ x (/ 1 x)))>
#<alt (+ x (/ 1 x))>
#<alt (/ 1 x)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt x>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(/ 1 (+ x (/ 1 x)))
0.0ms	x	@	0	(/ 1 (+ x (/ 1 x)))
0.0ms	x	@	inf	(/ 1 (+ x (/ 1 x)))
0.0ms	x	@	-inf	(+ x (/ 1 x))
0.0ms	x	@	0	(+ x (/ 1 x))

rewrite116.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1154×	`-lowering-.f32`
1154×	`-lowering-.f64`
1014×	`/-lowering-/.f32`
1014×	`/-lowering-/.f64`
446×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	37	11
2	284	11
0	2611	11

Stop Event

1×	iter limit
1×	iter limit
1×	node limit

Counts

3 → 166

Calls

Call 1

Inputs
(/ 1 (+ x (/ 1 x)))
(+ x (/ 1 x))
(/ 1 x)

Outputs
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))) (.f64 x x)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x)))) x) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x)))) (/.f64 #s(literal -1 binary64) x)))
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(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (-.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x) x)))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) x) x))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) x)) (.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) (+.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(/.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) x)
(/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (/.f64 #s(literal -1 binary64) x))) (.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (*.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) (+.f64 x (/.f64 #s(literal -1 binary64) x))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) x))) (+.f64 x (/.f64 #s(literal -1 binary64) x))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) x)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 x (/.f64 #s(literal -1 binary64) x))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (+.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x))) (neg.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 #s(literal -1 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) x)) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 #s(literal -1 binary64) x))) (/.f64 (.f64 x x) (+.f64 x (/.f64 #s(literal -1 binary64) x)))) (+.f64 (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) x))) (.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 #s(literal -1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) x))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 #s(literal -1 binary64) x))) (/.f64 (.f64 x x) (+.f64 x (/.f64 #s(literal -1 binary64) x)))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 #s(literal -1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) x))))
(/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))))
(/.f64 (.f64 (+.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x))))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) x) x))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))) (-.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x) x))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x)))) (+.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (pow.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x))))) (+.f64 x (/.f64 #s(literal -1 binary64) x)))
(pow.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) x) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) (+.f64 x (/.f64 #s(literal -1 binary64) x))))
(.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x)))))
(*.f64 #s(literal -1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) x) x))
(*.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))))
(.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(.f64 (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))))
(.f64 (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x))))
(.f64 (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x))) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x))) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))))
(.f64 (+.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))) (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x))) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)))
(.f64 (/.f64 (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 1 binary64)) (/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x))) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))) (+.f64 (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x))) (-.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))
(exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))

simplify189.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

2026×	`sum4-define`
1714×	`sum3-define`
1514×	`-lowering-.f32`
1514×	`-lowering-.f64`
1410×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	220
1	138	204
2	351	194
3	1066	173
4	3293	173
0	8187	173

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/ 1 x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x x)))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(+.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(+.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (pow x 2)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ (+ 1 (pow x 2)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ (+ 1 (pow x 2)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x)
x
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
x
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)

eval39.0ms (0.9%)

Compiler: Compiled 4569 to 486 computations (89.4% saved)

prune21.0ms (0.5%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	202	5	207

Accuracy

100.0%

Counts

207 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.9%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
✓	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	47.8%	(/.f64 #s(literal 1 binary64) x)
✓	53.3%	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
✓	53.8%	x

Compiler

Compiled 74 to 35 computations (52.7% saved)

regimes6.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) x)
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))

Calls

2 calls:

3.0ms	x
3.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes30.0ms (0.7%)

Counts

3 → 2

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) x)
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))

Outputs
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) x)

Calls

1 calls:

30.0ms

Results

Accuracy	Segments	Branch
98.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 2

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) x)

Outputs
x
(/.f64 #s(literal 1 binary64) x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
97.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
53.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch3.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.7915933038436065	0.9052857225950588

Results

1.0ms

32×

valid

Compiler

Compiled 40 to 28 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-div: 0.0ms (0% of total)

ival-add: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch11.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.9052857225950588	6516.400355652989

Results

6.0ms

128×

valid

Compiler

Compiled 76 to 56 computations (26.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 1.0ms (34.4% of total)

ival-add: 1.0ms (34.4% of total)

ival-mult: 1.0ms (34.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify23.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	23	30
2	30	30
3	34	30
4	36	30

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 1 binary64)) x (/.f64 #s(literal 1 binary64) x))
x

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 1 binary64)) x (/.f64 #s(literal 1 binary64) x))
x

soundness1.2s (29.2%)

Rules

3352×	`/-lowering-/.f32`
3352×	`/-lowering-/.f64`
2528×	`-lowering-.f32`
2528×	`-lowering-.f64`
2236×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	675
1	170	574
2	452	541
3	1623	538
4	6118	538
0	8107	538
0	5	13
1	31	13
2	207	13
3	1921	13
0	8610	13
0	45	211
1	137	195
2	355	185
3	1067	182
4	3300	182
0	8302	182

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 69 to 37 computations (46.4% saved)

preprocess38.0ms (0.9%)

Remove: (negabs x)
Compiler: Compiled 110 to 56 computations (49.1% saved)

x / (x^2 + 1)

analyze1.0ms (0%)

sample536.0ms (12.9%)

preprocess29.0ms (0.7%)

explain66.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize20.0ms (0.5%)

series2.0ms (0%)

rewrite297.0ms (7.2%)

simplify245.0ms (5.9%)

eval41.0ms (1%)

prune161.0ms (3.9%)

simplify131.0ms (3.2%)

localize62.0ms (1.5%)

series5.0ms (0.1%)

rewrite253.0ms (6.1%)

simplify196.0ms (4.7%)

eval302.0ms (7.3%)

prune82.0ms (2%)

simplify3.0ms (0.1%)

localize22.0ms (0.5%)

series1.0ms (0%)

rewrite116.0ms (2.8%)

simplify189.0ms (4.6%)

eval39.0ms (0.9%)

prune21.0ms (0.5%)

regimes6.0ms (0.1%)

regimes30.0ms (0.7%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch3.0ms (0.1%)

bsearch11.0ms (0.3%)

simplify23.0ms (0.5%)

soundness1.2s (29.2%)

preprocess38.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	19
1	30	19
2	68	18
3	146	18
4	304	18
5	549	18
6	872	18
7	874	18
8	898	18
9	914	18
0	5	6
1	9	6
0	9	6

Iter	Nodes	Cost
0	10	19
1	30	19
2	68	18
3	146	18
4	304	18
5	549	18
6	872	18
7	874	18
8	898	18
9	914	18
0	5	6
1	9	6
0	9	6

Iter	Nodes	Cost
0	10	19
1	30	19
2	68	18
3	146	18
4	304	18
5	549	18
6	872	18
7	874	18
8	898	18
9	914	18
0	5	6
1	9	6
0	9	6