Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample683.0ms (32.3%)

Results

670.0ms

8256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% saved)

preprocess16.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

34.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	32.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

1.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))	x	0
1.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))	x	-inf
1.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))	x	inf

rewrite35.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

488×	`log1p-expm1-u_binary64`
488×	`expm1-log1p-u_binary64`
476×	`unpow-prod-down_binary64`
289×	`log-prod_binary64`
142×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	122	6
2	1383	6

Stop Event

1×	node limit

Counts

1 → 55

simplify11.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

67 → 57

prune41.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	50	7	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	8	58

Error

0.1b

Counts

58 → 8

Alt Table

Status	Error	Program
	34.7b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	34.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	34.2b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 x x) 4))) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	40.7b	(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (pow.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (*.f64 x (sqrt.f64 2))) 1/2))
	29.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	33.9b	(*.f64 (sqrt.f64 2) x)
	34.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
▶	17.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

Compiler

Compiled 806 to 573 computations (28.9% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
✓	0.5b	(pow.f64 (cbrt.f64 x) 2)
✓	0.6b	(cbrt.f64 x)
✓	16.4b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

series135.0ms (6.4%)

Counts

4 → 12

Calls

12 calls:

49.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))	x	-inf
41.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)	x	-inf
19.0ms	(pow.f64 (cbrt.f64 x) 2)	x	-inf
8.0ms	(cbrt.f64 x)	x	-inf
5.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)	x	inf

rewrite46.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

824×	`expm1-log1p-u_binary64`
499×	`prod-diff_binary64`
99×	`log1p-expm1-u_binary64`
98×	`add-sqr-sqrt_binary64`
94×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	239	28
2	2699	28

Stop Event

1×	node limit

Counts

4 → 80

simplify11.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

92 → 83

prune55.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	108	9	117

Error

0.1b

Counts

117 → 9

Alt Table

Status	Error	Program
	34.7b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	34.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	17.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x))) (+.f64 x x)) 1/2))
	40.7b	(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (pow.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (*.f64 x (sqrt.f64 2))) 1/2))
	17.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)))
	29.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	33.9b	(*.f64 (sqrt.f64 2) x)
▶	17.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	17.7b	(.f64 (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

Compiler

Compiled 2012 to 1046 computations (48% saved)

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	0.6b	(cbrt.f64 x)
	16.4b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
✓	16.5b	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

series420.0ms (19.8%)

Counts

2 → 8

Calls

6 calls:

385.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))	x	-inf
30.0ms	(sqrt.f64 (*.f64 x (cbrt.f64 x)))	x	-inf
1.0ms	(sqrt.f64 (*.f64 x (cbrt.f64 x)))	x	0
1.0ms	(sqrt.f64 (*.f64 x (cbrt.f64 x)))	x	inf
1.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))	x	inf

rewrite43.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

918×	`prod-diff_binary64`
832×	`expm1-log1p-u_binary64`
105×	`add-sqr-sqrt_binary64`
103×	`log1p-expm1-u_binary64`
100×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	235	15
2	3018	15

Stop Event

1×	node limit

Counts

2 → 44

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	48
1	6	48

Stop Event

1×

saturated

Counts

52 → 45

prune57.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	116	10	126

Error

0.1b

Counts

126 → 10

Alt Table

Status	Error	Program
	34.7b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	17.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)))
✓	34.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	17.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x))) (+.f64 x x)) 1/2))
	40.7b	(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (pow.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (*.f64 x (sqrt.f64 2))) 1/2))
	29.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	33.9b	(*.f64 (sqrt.f64 2) x)
	17.3b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2))
✓	17.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	17.7b	(.f64 (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

Compiler

Compiled 2270 to 997 computations (56.1% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4))
	0.6b	(cbrt.f64 x)
	16.5b	(sqrt.f64 (*.f64 x (cbrt.f64 x)))
✓	16.6b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)

series43.0ms (2%)

Counts

2 → 0

Calls

6 calls:

17.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)	x	-inf
13.0ms	(.f64 (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4))	x	-inf
5.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)	x	inf
4.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)	x	0
2.0ms	(.f64 (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4))	x	0

rewrite40.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

719×	`log1p-expm1-u_binary64`
719×	`expm1-log1p-u_binary64`
425×	`prod-diff_binary64`
81×	`add-sqr-sqrt_binary64`
81×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	183	22
2	2333	22

Stop Event

1×	node limit

Counts

2 → 40

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

40 → 40

prune86.0ms (4.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	166	11	177

Error

0.1b

Counts

177 → 11

Alt Table

Status	Error	Program
	34.7b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	17.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)))
✓	34.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	17.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x))) (+.f64 x x)) 1/2))
	40.7b	(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (pow.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (*.f64 x (sqrt.f64 2))) 1/2))
	29.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	33.9b	(*.f64 (sqrt.f64 2) x)
	17.2b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4) (cbrt.f64 (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 3/4))))
	17.3b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2))
✓	17.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	17.7b	(.f64 (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

Compiler

Compiled 4626 to 1759 computations (62% saved)

regimes164.0ms (7.7%)

Accuracy

Total 0.3b remaining (74.1%)

Threshold costs 0.3b (74.1%)

Counts

35 → 2

Compiler

Compiled 1692 to 1115 computations (34.1% saved)

bsearch17.0ms (0.8%)

Algorithm

1×	binary-search

Calls

1 calls:

15.0ms

Steps

Iters	Point		Range
-1.23030379088895e-310	∈ [	-7.829812908509109e-305	,	3.2924902664946133e-307	]

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	22	25
2	30	25
3	36	25
4	39	25
5	40	25

Stop Event

1×

saturated

end145.0ms (6.8%)

Stop Event

1×

fuel

Compiler

Compiled 205 to 136 computations (33.7% saved)

Details

analyze4.0ms (0.2%)

sample683.0ms (32.3%)

preprocess16.0ms (0.8%)

simplify6.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite35.0ms (1.6%)

simplify11.0ms (0.5%)

prune41.0ms (1.9%)

localize10.0ms (0.5%)

series135.0ms (6.4%)

rewrite46.0ms (2.2%)

simplify11.0ms (0.5%)

prune55.0ms (2.6%)

localize12.0ms (0.6%)

series420.0ms (19.8%)

rewrite43.0ms (2%)

simplify7.0ms (0.3%)

prune57.0ms (2.7%)

localize12.0ms (0.5%)

series43.0ms (2%)

rewrite40.0ms (1.9%)

simplify6.0ms (0.3%)

prune86.0ms (4.1%)

regimes164.0ms (7.7%)

bsearch17.0ms (0.8%)

simplify3.0ms (0.1%)

end145.0ms (6.8%)

Profiling