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)

sample545.0ms (18.1%)

Results

390.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 196.0ms

ival-mult: 77.0ms (39.4% of total)

ival-div: 59.0ms (30.2% of total)

ival-add: 45.0ms (23% of total)

const: 11.0ms (5.6% of total)

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

Bogosity

preprocess29.0ms (1%)

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)

explain65.0ms (2.2%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
66	-	-	`(/.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

42.0ms

512×

valid

Compiler

Compiled 46 to 17 computations (63% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-add: 18.0ms (66.9% of total)

ival-mult: 5.0ms (18.6% of total)

ival-div: 4.0ms (14.9% of total)

const: 1.0ms (3.7% of total)

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

eval3.0ms (0.1%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.8%	(/.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	75.8%	(/.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% of total)

ival-mult: 2.0ms (33% of total)

ival-add: 1.0ms (16.5% 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	@	0	(+ (* x x) 1)

rewrite309.0ms (10.2%)

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))

simplify347.0ms (11.5%)

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)

eval46.0ms (1.5%)

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

prune40.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	355	3	358
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	355	4	359

Accuracy

100.0%

Counts

359 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.6%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
✓	75.8%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
▶	51.8%	(/.f64 #s(literal 1 binary64) x)
▶	50.8%	x

Compiler

Compiled 26 to 16 computations (38.5% saved)

simplify304.0ms (10.1%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64)))
✓	cost-diff	256	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)

Rules

5752×	`-lowering-.f32`
5752×	`-lowering-.f64`
3088×	`fma-define`
2932×	`fma-lowering-fma.f32`
2932×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	29
1	17	28
2	35	27
3	74	26
4	110	26
5	194	26
6	897	26
7	2238	26
8	3078	26
9	4204	26
10	5043	26
11	5317	26
12	5504	26
13	5665	26
14	5817	26
15	6765	26
16	7757	26
0	8055	26

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize38.0ms (1.3%)

Localize:

Found 5 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	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64)))
✓	accuracy	75.9%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)

Results

27.0ms

256×

valid

Compiler

Compiled 39 to 8 computations (79.5% saved)

Precisions

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

ival-div: 5.0ms (41.8% of total)

ival-add: 4.0ms (33.4% of total)

ival-mult: 2.0ms (16.7% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Counts

5 → 60

Calls

Call 1

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

Calls

15 calls:

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

rewrite261.0ms (8.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2032×	`-lowering-.f32`
2032×	`-lowering-.f64`
1682×	`/-lowering-/.f32`
1682×	`/-lowering-/.f64`
1602×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	53	20
2	346	19
3	3121	19
0	8236	19

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 308

Calls

Call 1

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

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

simplify392.0ms (13%)

Algorithm

1×	egg-herbie

Rules

2100×	`sum4-define`
1754×	`sum3-define`
1586×	`--lowering--.f32`
1586×	`--lowering--.f64`
1504×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	368
1	146	345
2	378	329
3	1165	321
4	3646	321
0	8365	321

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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

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

eval45.0ms (1.5%)

Compiler: Compiled 8716 to 1031 computations (88.2% saved)

prune50.0ms (1.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	404	0	404
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	404	4	408

Accuracy

100.0%

Counts

408 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	75.6%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
✓	75.8%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
✓	51.8%	(/.f64 #s(literal 1 binary64) x)
✓	50.8%	x

Compiler

Compiled 49 to 24 computations (51% saved)

regimes5.0ms (0.2%)

Counts

4 → 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 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))

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

Calls

2 calls:

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

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

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
98.8%	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
50.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch6.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
5.0ms	179.45250522461853	412115065.3884984

Results

3.0ms

64×

valid

Compiler

Compiled 68 to 48 computations (29.4% saved)

Precisions

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

ival-mult: 1.0ms (70.1% of total)

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

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

const: 0.0ms (0% of total)

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

bsearch13.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.014275317439438596	30.69229050516152

Results

8.0ms

128×

valid

Compiler

Compiled 76 to 56 computations (26.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-add: 3.0ms (60% of total)

ival-div: 1.0ms (20% of total)

ival-mult: 1.0ms (20% of total)

const: 0.0ms (0% of total)

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	15	23

Stop Event

1×

saturated

Calls

Call 1

Inputs

(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))

Outputs

(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))

soundness259.0ms (8.6%)

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 36 to 19 computations (47.2% saved)

preprocess217.0ms (7.2%)

Compiler: Compiled 110 to 60 computations (45.5% saved)

x / (x^2 + 1)

analyze1.0ms (0%)

sample545.0ms (18.1%)

preprocess29.0ms (1%)

explain65.0ms (2.2%)

eval3.0ms (0.1%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize20.0ms (0.7%)

series2.0ms (0.1%)

rewrite309.0ms (10.2%)

simplify347.0ms (11.5%)

eval46.0ms (1.5%)

prune40.0ms (1.3%)

simplify304.0ms (10.1%)

localize38.0ms (1.3%)

series2.0ms (0.1%)

rewrite261.0ms (8.7%)

simplify392.0ms (13%)

eval45.0ms (1.5%)

prune50.0ms (1.7%)

regimes5.0ms (0.2%)

regimes2.0ms (0.1%)

regimes1.0ms (0%)

bsearch6.0ms (0.2%)

bsearch13.0ms (0.4%)

simplify7.0ms (0.2%)

soundness259.0ms (8.6%)

preprocess217.0ms (7.2%)

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