Metrics for math.cube on real

analyze0.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 7 to 4 computations (42.9% saved)

Precisions

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

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

const: 0.0ms (0% of total)

sample683.0ms (48.8%)

Results

346.0ms	5474×	0	valid
167.0ms	2782×	0	infinite

Precisions

Click to see histograms. Total time spent on operations: 160.0ms

ival-mult: 149.0ms (93% of total)

const: 7.0ms (4.4% of total)

backward-pass: 4.0ms (2.5% of total)

Bogosity

preprocess39.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-define`
15×	`associate-r`
12×	`fma-neg`
9×	`distribute-lft-neg-in`
8×	`unsub-neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	92
1	30	44
2	66	44
3	143	44
4	182	44
5	216	44

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)
(.f64 (.f64 x x) x)
(.f64 (.f64 (neg.f64 x) (neg.f64 x)) (neg.f64 x))
(neg.f64 (.f64 (.f64 (neg.f64 x) (neg.f64 x)) (neg.f64 x)))

Outputs
(.f64 (.f64 x x) x)
(pow.f64 x #s(literal 3 binary64))
(.f64 (.f64 x x) x)
(pow.f64 x #s(literal 3 binary64))
(.f64 (.f64 (neg.f64 x) (neg.f64 x)) (neg.f64 x))
(pow.f64 (neg.f64 x) #s(literal 3 binary64))
(neg.f64 (.f64 (.f64 (neg.f64 x) (neg.f64 x)) (neg.f64 x)))
(pow.f64 x #s(literal 3 binary64))

Symmetry

(negabs x)

explain52.0ms (3.7%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(*.f64 x x)`
-	-	`(.f64 (.f64 x x) x)`

Results

21.0ms	346×	256	valid
17.0ms	166×	256	infinite

Compiler

Compiled 28 to 11 computations (60.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 12.0ms (92.6% of total)

const: 1.0ms (7.7% of total)

eval0.0ms (0%)

Compiler: Compiled 4 to 3 computations (25% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 x #s(literal 3 binary64))
▶	99.9%	(.f64 (.f64 x x) x)

Compiler

Compiled 10 to 6 computations (40% saved)

localize32.0ms (2.3%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.9%	(.f64 (.f64 x x) x)

Results

17.0ms	173×	256	valid
7.0ms	83×	256	infinite

Compiler

Compiled 16 to 7 computations (56.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 4.0ms (47.6% of total)

ival-pow: 4.0ms (47.6% of total)

const: 0.0ms (0% of total)

series2.0ms (0.1%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (.f64 (.f64 x x) x)>

Outputs
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>
#<alt (pow.f64 x #s(literal 3 binary64))>

Calls

3 calls:

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

rewrite316.0ms (22.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1115×	`log1p-expm1-u`
308×	`associate-r`
223×	`associate-l`
197×	`unpow-prod-down`
190×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	66	10
2	617	10
3	6336	10

Stop Event

1×	node limit

Counts

1 → 58

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)

Outputs
(+.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (E.f64) (.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))))) (log.f64 (cbrt.f64 (exp.f64 (.f64 x (*.f64 x x))))))
(+.f64 (log.f64 (pow.f64 (E.f64) (/.f64 (.f64 x (.f64 x x)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (E.f64) (/.f64 (.f64 x (.f64 x x)) #s(literal 2 binary64)))))
(-.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x (*.f64 x x)) (log.f64 (E.f64)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 (cbrt.f64 (.f64 x x)) (.f64 (.f64 x x) (cbrt.f64 x)))
(.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (*.f64 x x) #s(literal 5/6 binary64)))
(.f64 (cbrt.f64 x) (.f64 x (pow.f64 (*.f64 x x) #s(literal 5/6 binary64))))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 x #s(literal 1/6 binary64)) (pow.f64 x #s(literal 5/2 binary64))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 5/2 binary64)))
(.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (.f64 x x) (cbrt.f64 x))))
(.f64 (.f64 x (pow.f64 (*.f64 x x) #s(literal 5/6 binary64))) (cbrt.f64 x))
(.f64 (cbrt.f64 (.f64 x (pow.f64 (.f64 x x) #s(literal 5/6 binary64)))) (.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) (pow.f64 (.f64 x x) #s(literal 5/6 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/2 binary64))))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 9/2 binary64))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (.f64 (.f64 x x) (cbrt.f64 x)) (cbrt.f64 (.f64 x x)))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 x x) #s(literal 5/6 binary64)) (*.f64 x (cbrt.f64 x)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 15/2 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 x))
(.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (sqrt.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (cbrt.f64 x)))) (cbrt.f64 x))
(.f64 (.f64 (.f64 (.f64 x x) (cbrt.f64 x)) (cbrt.f64 (.f64 x (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 (.f64 x x))))
(.f64 (.f64 (.f64 x (pow.f64 (.f64 x x) #s(literal 5/6 binary64))) (cbrt.f64 (cbrt.f64 (*.f64 x x)))) (cbrt.f64 (cbrt.f64 x)))
(.f64 (.f64 (.f64 x (pow.f64 (.f64 x x) #s(literal 5/6 binary64))) (pow.f64 x #s(literal 1/6 binary64))) (pow.f64 x #s(literal 1/6 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 5/2 binary64)) (cbrt.f64 x)) (pow.f64 x #s(literal 1/6 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 5/2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (+.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 x) #s(literal 9 binary64))
(pow.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 6 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))))) #s(literal 1/3 binary64))
(pow.f64 (E.f64) (*.f64 #s(literal 3 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (.f64 #s(literal 3 binary64) (log.f64 x))) #s(literal 2 binary64))) (cbrt.f64 (.f64 #s(literal 3 binary64) (log.f64 x))))
(pow.f64 (exp.f64 (pow.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64))) (pow.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (*.f64 x x)))))
(fabs.f64 (.f64 x (.f64 x x)))
(log.f64 (exp.f64 (.f64 x (.f64 x x))))
(cbrt.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))))))
(expm1.f64 (log1p.f64 (.f64 x (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 x x))))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (*.f64 #s(literal 3 binary64) (log.f64 x))) #s(literal 1/3 binary64)))

simplify175.0ms (12.5%)

Algorithm

1×	egg-herbie

Rules

516×	`associate-r`
365×	`fma-define`
338×	`distribute-lft-in`
333×	`associate-+l-`
307×	`associate-+r-`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	1641
1	310	1632
2	890	1612
3	3740	1543
4	7728	1543

Stop Event

1×	node limit

Counts

70 → 68

Calls

Call 1

Inputs
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 x #s(literal 3 binary64))
(+.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (E.f64) (.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))))) (log.f64 (cbrt.f64 (exp.f64 (.f64 x (*.f64 x x))))))
(+.f64 (log.f64 (pow.f64 (E.f64) (/.f64 (.f64 x (.f64 x x)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (E.f64) (/.f64 (.f64 x (.f64 x x)) #s(literal 2 binary64)))))
(-.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x (*.f64 x x)) (log.f64 (E.f64)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 (cbrt.f64 (.f64 x x)) (.f64 (.f64 x x) (cbrt.f64 x)))
(.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (*.f64 x x) #s(literal 5/6 binary64)))
(.f64 (cbrt.f64 x) (.f64 x (pow.f64 (*.f64 x x) #s(literal 5/6 binary64))))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 x #s(literal 1/6 binary64)) (pow.f64 x #s(literal 5/2 binary64))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 5/2 binary64)))
(.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (.f64 x x) (cbrt.f64 x))))
(.f64 (.f64 x (pow.f64 (*.f64 x x) #s(literal 5/6 binary64))) (cbrt.f64 x))
(.f64 (cbrt.f64 (.f64 x (pow.f64 (.f64 x x) #s(literal 5/6 binary64)))) (.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) (pow.f64 (.f64 x x) #s(literal 5/6 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/2 binary64))))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 9/2 binary64))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (.f64 (.f64 x x) (cbrt.f64 x)) (cbrt.f64 (.f64 x x)))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 x x) #s(literal 5/6 binary64)) (*.f64 x (cbrt.f64 x)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 15/2 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 x))
(.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (sqrt.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (cbrt.f64 x)))) (cbrt.f64 x))
(.f64 (.f64 (.f64 (.f64 x x) (cbrt.f64 x)) (cbrt.f64 (.f64 x (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 (.f64 x x))))
(.f64 (.f64 (.f64 x (pow.f64 (.f64 x x) #s(literal 5/6 binary64))) (cbrt.f64 (cbrt.f64 (*.f64 x x)))) (cbrt.f64 (cbrt.f64 x)))
(.f64 (.f64 (.f64 x (pow.f64 (.f64 x x) #s(literal 5/6 binary64))) (pow.f64 x #s(literal 1/6 binary64))) (pow.f64 x #s(literal 1/6 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 5/2 binary64)) (cbrt.f64 x)) (pow.f64 x #s(literal 1/6 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 5/2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (+.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 x) #s(literal 9 binary64))
(pow.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 6 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))))) #s(literal 1/3 binary64))
(pow.f64 (E.f64) (*.f64 #s(literal 3 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (.f64 #s(literal 3 binary64) (log.f64 x))) #s(literal 2 binary64))) (cbrt.f64 (.f64 #s(literal 3 binary64) (log.f64 x))))
(pow.f64 (exp.f64 (pow.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64))) (pow.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (*.f64 x x)))))
(fabs.f64 (.f64 x (.f64 x x)))
(log.f64 (exp.f64 (.f64 x (.f64 x x))))
(cbrt.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))))))
(expm1.f64 (log1p.f64 (.f64 x (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 x x))))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (*.f64 #s(literal 3 binary64) (log.f64 x))) #s(literal 1/3 binary64)))

Outputs
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(+.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 x (.f64 x x))
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(.f64 x (.f64 x x))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (E.f64) (.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))))) (log.f64 (cbrt.f64 (exp.f64 (.f64 x (*.f64 x x))))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (E.f64) (.f64 (.f64 x x) (.f64 x #s(literal 2 binary64)))))) (log.f64 (cbrt.f64 (exp.f64 (.f64 x (*.f64 x x))))))
(+.f64 (log.f64 (pow.f64 (E.f64) (/.f64 (.f64 x (.f64 x x)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (E.f64) (/.f64 (.f64 x (.f64 x x)) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (log.f64 (pow.f64 (E.f64) (.f64 x (*.f64 x (/.f64 x #s(literal 2 binary64)))))))
(-.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 x (.f64 x x))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x (*.f64 x x)) (log.f64 (E.f64)))
(.f64 x (.f64 x x))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 x (.f64 x x))
(.f64 (cbrt.f64 (.f64 x x)) (.f64 (.f64 x x) (cbrt.f64 x)))
(.f64 x (.f64 (cbrt.f64 (.f64 x x)) (.f64 x (cbrt.f64 x))))
(.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (*.f64 x x) #s(literal 5/6 binary64)))
(.f64 (cbrt.f64 x) (.f64 x (pow.f64 (*.f64 x x) #s(literal 5/6 binary64))))
(.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (*.f64 x x) #s(literal 5/6 binary64)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 x #s(literal 1/6 binary64)) (pow.f64 x #s(literal 5/2 binary64))))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/6 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 x (.f64 x x))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 5/2 binary64)))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))
(.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (.f64 x x) (cbrt.f64 x))))
(.f64 (.f64 x (.f64 x (cbrt.f64 x))) (.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 (.f64 x x)))))
(.f64 (.f64 x (pow.f64 (*.f64 x x) #s(literal 5/6 binary64))) (cbrt.f64 x))
(.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (*.f64 x x) #s(literal 5/6 binary64)))
(.f64 (cbrt.f64 (.f64 x (pow.f64 (.f64 x x) #s(literal 5/6 binary64)))) (.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) (pow.f64 (.f64 x x) #s(literal 5/6 binary64))))
(.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) (.f64 (pow.f64 (.f64 x x) #s(literal 5/6 binary64)) (cbrt.f64 (.f64 x (pow.f64 (.f64 x x) #s(literal 5/6 binary64))))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/2 binary64))))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 9/2 binary64))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 x (.f64 x x))
(.f64 (.f64 (.f64 x x) (cbrt.f64 x)) (cbrt.f64 (.f64 x x)))
(.f64 x (.f64 (cbrt.f64 (.f64 x x)) (.f64 x (cbrt.f64 x))))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 x x) #s(literal 5/6 binary64)) (*.f64 x (cbrt.f64 x)))
(.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (*.f64 x x) #s(literal 5/6 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)))
(.f64 x (.f64 x x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 15/2 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 x #s(literal 15/2 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 x (.f64 x x))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 9/2 binary64))))
(.f64 (sqrt.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (cbrt.f64 x)))) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x (cbrt.f64 x))))))))
(.f64 (.f64 (.f64 (.f64 x x) (cbrt.f64 x)) (cbrt.f64 (.f64 x (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 (.f64 x x))))
(.f64 (.f64 x (.f64 x (cbrt.f64 x))) (.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 (.f64 x x)))))
(.f64 (.f64 (.f64 x (pow.f64 (.f64 x x) #s(literal 5/6 binary64))) (cbrt.f64 (cbrt.f64 (*.f64 x x)))) (cbrt.f64 (cbrt.f64 x)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (.f64 x (cbrt.f64 (cbrt.f64 x))) (pow.f64 (*.f64 x x) #s(literal 5/6 binary64))))
(.f64 (.f64 (.f64 x (pow.f64 (.f64 x x) #s(literal 5/6 binary64))) (pow.f64 x #s(literal 1/6 binary64))) (pow.f64 x #s(literal 1/6 binary64)))
(.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (*.f64 x x) #s(literal 5/6 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 5/2 binary64)) (cbrt.f64 x)) (pow.f64 x #s(literal 1/6 binary64)))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/6 binary64)) #s(literal 3 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 5/2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (+.f64 (.f64 x (*.f64 x x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (+.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(.f64 x (.f64 x x))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(.f64 x (.f64 x x))
(pow.f64 (cbrt.f64 x) #s(literal 9 binary64))
(.f64 x (.f64 x x))
(pow.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(.f64 x (.f64 x x))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(.f64 x (.f64 x x))
(pow.f64 (sqrt.f64 x) #s(literal 6 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))))) #s(literal 1/3 binary64))
(.f64 x (.f64 x x))
(pow.f64 (E.f64) (*.f64 #s(literal 3 binary64) (log.f64 x)))
(.f64 x (.f64 x x))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(.f64 x (.f64 x x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (.f64 #s(literal 3 binary64) (log.f64 x))) #s(literal 2 binary64))) (cbrt.f64 (.f64 #s(literal 3 binary64) (log.f64 x))))
(pow.f64 (exp.f64 (pow.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64))) (pow.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (*.f64 x x)))))
(.f64 x (.f64 x x))
(fabs.f64 (.f64 x (.f64 x x)))
(.f64 x (.f64 x x))
(log.f64 (exp.f64 (.f64 x (.f64 x x))))
(.f64 x (.f64 x x))
(cbrt.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))))))
(.f64 x (.f64 x x))
(expm1.f64 (log1p.f64 (.f64 x (.f64 x x))))
(.f64 x (.f64 x x))
(log1p.f64 (expm1.f64 (.f64 x (.f64 x x))))
(.f64 x (.f64 x x))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(.f64 x (.f64 x x))
(exp.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(.f64 x (.f64 x x))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (*.f64 #s(literal 3 binary64) (log.f64 x))) #s(literal 1/3 binary64)))
(.f64 x (.f64 x x))

eval27.0ms (1.9%)

Compiler: Compiled 1450 to 586 computations (59.6% saved)

prune12.0ms (0.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	138	2	140

Accuracy

100.0%

Counts

140 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 x #s(literal 3 binary64))
✓	99.9%	(.f64 (.f64 x x) x)

Compiler

Compiled 19 to 11 computations (42.1% saved)

regimes2.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)
(pow.f64 x #s(literal 3 binary64))

Outputs
(pow.f64 x #s(literal 3 binary64))

Calls

2 calls:

1.0ms	x
1.0ms	(.f64 (.f64 x x) x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(.f64 (.f64 x x) x)`

Compiler

Compiled 8 to 4 computations (50% saved)

regimes1.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)

Outputs
(.f64 (.f64 x x) x)

Calls

2 calls:

0.0ms	(.f64 (.f64 x x) x)
0.0ms	x

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(.f64 (.f64 x x) x)`

Compiler

Compiled 8 to 4 computations (50% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	10	32

Stop Event

1×

saturated

Calls

Call 1

Inputs
(pow.f64 x #s(literal 3 binary64))
(.f64 (.f64 x x) x)

Outputs
(pow.f64 x #s(literal 3 binary64))
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))

soundness15.0ms (1%)

Rules

32×	`fma-define`
15×	`associate-r`
12×	`fma-neg`
9×	`distribute-lft-neg-in`
8×	`unsub-neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	92
1	30	44
2	66	44
3	143	44
4	182	44
5	216	44

Stop Event

1×	done
1×	saturated

Compiler

Compiled 18 to 10 computations (44.4% saved)

preprocess39.0ms (2.8%)

Remove: (negabs x)
Compiler: Compiled 62 to 40 computations (35.5% saved)

math.cube on real

analyze0.0ms (0%)

sample683.0ms (48.8%)

preprocess39.0ms (2.8%)

explain52.0ms (3.7%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize32.0ms (2.3%)

series2.0ms (0.1%)

rewrite316.0ms (22.6%)

simplify175.0ms (12.5%)

eval27.0ms (1.9%)

prune12.0ms (0.9%)

regimes2.0ms (0.2%)

regimes1.0ms (0.1%)

simplify3.0ms (0.2%)

soundness15.0ms (1%)

preprocess39.0ms (2.8%)

end0.0ms (0%)

Profiling