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)

sample522.0ms (17.4%)

Results

366.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 201.0ms

ival-mult: 79.0ms (39.4% of total)

ival-div: 64.0ms (31.9% of total)

ival-add: 44.0ms (21.9% of total)

const: 11.0ms (5.5% of total)

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

Bogosity

preprocess42.0ms (1.4%)

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)

explain51.0ms (1.7%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
79	-	-	`(/.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 (42.1% of total)

ival-div: 4.0ms (33.7% of total)

ival-add: 3.0ms (25.3% of total)

const: 1.0ms (8.4% of total)

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

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.2%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify3.0ms (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 (0.7%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	71.2%	(/.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 (33.6% of total)

ival-mult: 2.0ms (33.6% of total)

ival-add: 1.0ms (16.8% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0.1%)

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	@	0	(/ x (+ (* x x) 1))
0.0ms	x	@	-inf	(/ x (+ (* x x) 1))
0.0ms	x	@	inf	(+ (* x x) 1)
0.0ms	x	@	inf	(* x x)

rewrite308.0ms (10.3%)

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))

simplify331.0ms (11.1%)

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)

eval38.0ms (1.3%)

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

prune43.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	354	4	358
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	354	5	359

Accuracy

100.0%

Counts

359 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.3%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
▶	55.6%	(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
✓	71.2%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
▶	58.1%	(/.f64 #s(literal 1 binary64) x)
▶	44.7%	x

Compiler

Compiled 42 to 25 computations (40.5% saved)

simplify168.0ms (5.6%)

Algorithm

1×	egg-herbie

Localize:

Found 9 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 (*.f64 x x) #s(literal -1 binary64))
✓	cost-diff	0	(.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))
✓	cost-diff	640	(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)

Rules

3092×	`-lowering-.f32`
3092×	`-lowering-.f64`
1680×	`sum3-define`
1546×	`fnmadd-define`
1540×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	74
1	40	70
2	68	68
3	149	63
4	499	63
5	3372	63
0	8221	63

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize73.0ms (2.4%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
✓	accuracy	99.5%	(/.f64 #s(literal -1 binary64) (*.f64 x x))
✓	accuracy	99.9%	(.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))
✓	accuracy	99.9%	(.f64 x (.f64 x (*.f64 x x)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	56.4%	(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)

Results

39.0ms

256×

valid

Compiler

Compiled 90 to 15 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-div: 7.0ms (37.9% of total)

ival-mult: 7.0ms (37.9% of total)

ival-add: 4.0ms (21.6% of total)

const: 1.0ms (5.4% of total)

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

series6.0ms (0.2%)

Counts

10 → 120

Calls

Call 1

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

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

Calls

30 calls:

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

rewrite483.0ms (16.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4054×	`-lowering-.f32`
4054×	`-lowering-.f64`
3776×	`/-lowering-/.f32`
3776×	`/-lowering-/.f64`
1222×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	57
1	103	46
2	777	42
0	8475	42

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 543

Calls

Call 1

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

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

simplify199.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

2796×	`-lowering-.f32`
2796×	`-lowering-.f64`
1326×	`/-lowering-/.f32`
1326×	`/-lowering-/.f64`
1136×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	607
1	156	542
2	416	527
3	1484	524
4	5506	524
0	8203	524

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

eval81.0ms (2.7%)

Compiler: Compiled 18408 to 1733 computations (90.6% saved)

prune91.0ms (3%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	725	0	725
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	725	5	730

Accuracy

100.0%

Counts

730 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.3%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
✓	55.6%	(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
✓	71.2%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
✓	58.1%	(/.f64 #s(literal 1 binary64) x)
✓	44.7%	x

Compiler

Compiled 80 to 41 computations (48.8% saved)

regimes6.0ms (0.2%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
2.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
100.0%	2	`x`
99.9%	2	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes2.0ms (0.1%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
100.0%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0.1%)

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:

1.0ms

Results

Accuracy	Segments	Branch
99.2%	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
44.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch9.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
7.0ms	2.7002443921141444	12700.235491779962

Results

4.0ms

96×

valid

Compiler

Compiled 132 to 92 computations (30.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (44.2% of total)

ival-add: 1.0ms (44.2% of total)

ival-mult: 1.0ms (44.2% of total)

const: 0.0ms (0% of total)

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

bsearch2.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	67039391.56025427	98660736064.65666

Results

1.0ms

16×

valid

Compiler

Compiled 26 to 18 computations (30.8% 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)

bsearch9.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	0.15474961482396637	2.7002443921141444

Results

5.0ms

112×

valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (40.2% of total)

ival-add: 1.0ms (40.2% of total)

ival-mult: 1.0ms (40.2% of total)

const: 0.0ms (0% of total)

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

simplify18.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	23	43

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 10000 binary64)) (/.f64 x (+.f64 (.f64 x x) #s(literal 1 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) x))
(if (<=.f64 x #s(literal 100000000 binary64)) (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 1 binary64)) x (/.f64 #s(literal 1 binary64) x))
x

Outputs
(if (<=.f64 x #s(literal 10000 binary64)) (/.f64 x (+.f64 (.f64 x x) #s(literal 1 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) x))
(if (<=.f64 x #s(literal 100000000 binary64)) (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 1 binary64)) x (/.f64 #s(literal 1 binary64) x))
x

soundness400.0ms (13.3%)

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×	done
1×	iter limit
1×	node limit

Compiler

Compiled 66 to 33 computations (50% saved)

preprocess84.0ms (2.8%)

Compiler: Compiled 162 to 80 computations (50.6% saved)

x / (x^2 + 1)

analyze1.0ms (0%)

sample522.0ms (17.4%)

preprocess42.0ms (1.4%)

explain51.0ms (1.7%)

eval0.0ms (0%)

prune3.0ms (0.1%)

simplify3.0ms (0.1%)

localize20.0ms (0.7%)

series2.0ms (0.1%)

rewrite308.0ms (10.3%)

simplify331.0ms (11.1%)

eval38.0ms (1.3%)

prune43.0ms (1.4%)

simplify168.0ms (5.6%)

localize73.0ms (2.4%)

series6.0ms (0.2%)

rewrite483.0ms (16.1%)

simplify199.0ms (6.6%)

eval81.0ms (2.7%)

prune91.0ms (3%)

regimes6.0ms (0.2%)

regimes2.0ms (0.1%)

regimes2.0ms (0.1%)

regimes1.0ms (0%)

bsearch9.0ms (0.3%)

bsearch2.0ms (0.1%)

bsearch9.0ms (0.3%)

simplify18.0ms (0.6%)

soundness400.0ms (13.3%)

preprocess84.0ms (2.8%)

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