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)

sample651.0ms (33.7%)

Results

623.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% 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

31.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.6b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	30.4b	(sqrt.f64 (.f64 (.f64 2 x) x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(sqrt.f64 (*.f64 (*.f64 2 x) x))

rewrite41.0ms (2.1%)

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

Calls

1 calls:

40.0ms

(sqrt.f64 (*.f64 (*.f64 2 x) x))

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

prune30.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	6	58

Error

0.1b

Counts

58 → 6

Alt Table

Status	Error	Program
✓	31.6b	(sqrt.f64 (.f64 (.f64 2 x) x))
	35.6b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
▶	15.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	35.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	35.1b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 734 to 517 computations (29.6% saved)

localize11.0ms (0.6%)

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)
✓	15.1b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

series95.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
28.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
20.0ms	(pow.f64 (cbrt.f64 x) 2)
10.0ms	(cbrt.f64 x)

rewrite44.0ms (2.3%)

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

Calls

4 calls:

43.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
43.0ms	(pow.f64 (cbrt.f64 x) 2)
43.0ms	(cbrt.f64 x)
43.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

simplify11.0ms (0.6%)

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

prune63.0ms (3.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	107	8	115

Error

0.1b

Counts

115 → 8

Alt Table

Status	Error	Program
✓	31.6b	(sqrt.f64 (.f64 (.f64 2 x) x))
	15.9b	(.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)))
	35.6b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
▶	15.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
✓	15.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	35.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	35.1b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 1925 to 984 computations (48.9% saved)

localize11.0ms (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)
	15.1b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
✓	15.1b	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

series423.0ms (21.9%)

Counts

2 → 8

Calls

2 calls:

390.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
33.0ms	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

rewrite42.0ms (2.2%)

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

Calls

2 calls:

41.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
41.0ms	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

simplify7.0ms (0.4%)

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

prune53.0ms (2.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	117	8	125

Error

0.1b

Counts

125 → 8

Alt Table

Status	Error	Program
✓	31.6b	(sqrt.f64 (.f64 (.f64 2 x) x))
	35.6b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	15.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
✓	15.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	35.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	15.6b	(.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)))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	35.1b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 2145 to 909 computations (57.6% saved)

localize13.0ms (0.7%)

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)
	15.1b	(sqrt.f64 (*.f64 x (cbrt.f64 x)))
✓	15.2b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)

series38.0ms (2%)

Counts

2 → 0

Calls

2 calls:

24.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)
14.0ms	(.f64 (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4))

rewrite41.0ms (2.1%)

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

Calls

2 calls:

40.0ms	(.f64 (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4))
40.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)

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

prune91.0ms (4.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	166	9	175

Error

0.1b

Counts

175 → 9

Alt Table

Status	Error	Program
✓	31.6b	(sqrt.f64 (.f64 (.f64 2 x) x))
	35.6b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	15.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	15.7b	(.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 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/4)))
✓	15.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	35.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	15.6b	(.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)))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	35.1b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 4573 to 1723 computations (62.3% saved)

regimes89.0ms (4.6%)

Accuracy

Total 0.3b remaining (72.5%)

Threshold costs 0.3b (72.5%)

Counts

27 → 2

Compiler

Compiled 1329 to 887 computations (33.3% saved)

bsearch16.0ms (0.8%)

Steps

Iters	Range		Point
10	-5.599572924662996e-308	5.503625174824193e-298	1.29087552084645e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.3%)

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

end118.0ms (6.1%)

Compiler: Compiled 152 to 100 computations (34.2% saved)

Details

analyze4.0ms (0.2%)

sample651.0ms (33.7%)

simplify6.0ms (0.3%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

series3.0ms (0.1%)

rewrite41.0ms (2.1%)

simplify11.0ms (0.5%)

prune30.0ms (1.6%)

localize11.0ms (0.6%)

series95.0ms (4.9%)

rewrite44.0ms (2.3%)

simplify11.0ms (0.6%)

prune63.0ms (3.3%)

localize11.0ms (0.6%)

series423.0ms (21.9%)

rewrite42.0ms (2.2%)

simplify7.0ms (0.4%)

prune53.0ms (2.8%)

localize13.0ms (0.7%)

series38.0ms (2%)

rewrite41.0ms (2.1%)

simplify6.0ms (0.3%)

prune91.0ms (4.7%)

regimes89.0ms (4.6%)

bsearch16.0ms (0.8%)

simplify6.0ms (0.3%)

end118.0ms (6.1%)

Profiling