Details

analyze4.0ms (0.1%)

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)

sample694.0ms (14.9%)

Results

666.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9
3	11	9

prune2.0ms (0%)

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

31.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.4b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	30.1b	(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))

rewrite38.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

1 → 55

Calls

1 calls:

37.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	121	6
2	1317	6
3	4961	6
0	0	0
1	0	0

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

67 → 57

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	24	80
3	25	80
4	29	80
5	47	80
6	58	80
7	63	80
8	75	80
9	72	80
10	58	80

prune34.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	49	8	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	9	58

Error

0.1b

Counts

58 → 9

Alt Table

Status	Error	Program
	33.4b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	31.4b	(sqrt.f64 (.f64 (.f64 2 x) x))
	15.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
▶	15.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	40.1b	(.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))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.9b	(*.f64 (sqrt.f64 2) x)
	33.6b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.3b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 822 to 555 computations (32.5% saved)

localize12.0ms (0.3%)

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)
✓	0.5b	(cbrt.f64 x)
✓	14.4b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

series804.0ms (17.3%)

Counts

4 → 48

Calls

4 calls:

719.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
38.0ms	(pow.f64 (cbrt.f64 x) 2)
30.0ms	(cbrt.f64 x)
17.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

rewrite81.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

824×	`log1p-expm1-u_binary64`
824×	`expm1-log1p-u_binary64`
499×	`prod-diff_binary64`
99×	`add-sqr-sqrt_binary64`
93×	`add-cube-cbrt_binary64`

Counts

4 → 80

Calls

4 calls:

79.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
79.0ms	(pow.f64 (cbrt.f64 x) 2)
79.0ms	(cbrt.f64 x)
79.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	219	25
2	2178	25
3	5792	25
0	0	0
1	0	0

simplify132.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

927×	`fma-def_binary64`
735×	`sqr-pow_binary64`
412×	`unswap-sqr_binary64`
388×	`*-commutative_binary64`
288×	`fma-neg_binary64`

Counts

128 → 93

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	400
1	53	400
2	100	400
3	234	400
4	671	400
5	1071	400
6	1134	400
7	1347	400
8	1640	400
9	1962	400
10	2318	400
11	2672	400
12	3136	400
13	3857	400
14	4627	400
15	4938	400
16	4746	400

prune104.0ms (2.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	121	10	131

Error

0.1b

Counts

131 → 10

Alt Table

Status	Error	Program
	33.4b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	31.4b	(sqrt.f64 (.f64 (.f64 2 x) x))
	15.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	15.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
✓	15.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	40.1b	(.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))
	32.9b	(*.f64 (sqrt.f64 2) x)
	33.6b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.3b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 2128 to 1269 computations (40.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
✓	0.5b	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
✓	0.6b	(cbrt.f64 (+.f64 x x))
✓	14.5b	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)

series951.0ms (20.4%)

Counts

4 → 48

Calls

4 calls:

848.0ms	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)
46.0ms	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
34.0ms	(cbrt.f64 (+.f64 x x))
23.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))

rewrite63.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
308×	`log-prod_binary64`
238×	`prod-diff_binary64`
218×	`egg-rr`

Counts

4 → 218

Calls

4 calls:

60.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
60.0ms	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
60.0ms	(cbrt.f64 (+.f64 x x))
60.0ms	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	215	26
2	1624	26
3	4958	26
0	0	0
1	0	0

simplify117.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-def_binary64`
790×	`unswap-sqr_binary64`
662×	`sqr-pow_binary64`
468×	`*-commutative_binary64`
344×	`distribute-rgt-in_binary64`

Counts

266 → 139

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	516
1	64	516
2	129	516
3	324	516
4	1021	516
5	1715	516
6	1918	516
7	2288	516
8	2999	516
9	3608	516
10	4272	516
11	4564	516
12	4655	516

prune98.0ms (2.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	232	11	243

Error

0.1b

Counts

243 → 11

Alt Table

Status	Error	Program
▶	15.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2))
✓	15.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	33.4b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	31.4b	(sqrt.f64 (.f64 (.f64 2 x) x))
	15.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	15.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	40.1b	(.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))
	32.9b	(*.f64 (sqrt.f64 2) x)
	33.6b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.3b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 5034 to 2323 computations (53.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 x)
	0.6b	(cbrt.f64 (+.f64 x x))
✓	1.0b	(cbrt.f64 2)
✓	14.5b	(pow.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2)

series964.0ms (20.7%)

Counts

2 → 12

Calls

2 calls:

964.0ms	(pow.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2)
0.0ms	(cbrt.f64 2)

rewrite42.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

716×	`log1p-expm1-u_binary64`
716×	`expm1-log1p-u_binary64`
142×	`expm1-udef_binary64`
142×	`log1p-udef_binary64`
133×	`log-pow_binary64`

Counts

2 → 40

Calls

2 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	184	14
2	1903	14
3	4889	14
0	0	0
1	0	0

simplify139.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1024×	`sqr-pow_binary64`
744×	`fabs-mul_binary64`
722×	`cube-prod_binary64`
450×	`unswap-sqr_binary64`
390×	`pow-sqr_binary64`

Counts

52 → 44

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	184
1	32	184
2	62	184
3	99	184
4	192	184
5	464	184
6	641	184
7	1056	184
8	1095	184
9	1271	184
10	1472	184
11	1756	184
12	2046	184
13	2468	184
14	3023	184
15	3312	184
16	3602	184
17	3770	184
18	3845	184
19	3912	184
20	4688	184
21	4787	184

prune94.0ms (2%)

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	1	2	3
Total	167	11	178

Error

0.1b

Counts

178 → 11

Alt Table

Status	Error	Program
	33.4b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	31.4b	(sqrt.f64 (.f64 (.f64 2 x) x))
	40.1b	(.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))
	15.6b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (.f64 (cbrt.f64 (.f64 x (cbrt.f64 (.f64 2 x)))) (cbrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 (.f64 2 x)))))))
	15.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	15.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
✓	15.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2))
	32.9b	(*.f64 (sqrt.f64 2) x)
	33.6b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.3b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 3730 to 2350 computations (37% saved)

regimes82.0ms (1.8%)

Accuracy

Total 0.3b remaining (72.3%)

Threshold costs 0.3b (72.3%)

Counts

22 → 2

Compiler

Compiled 906 to 659 computations (27.3% saved)

bsearch15.0ms (0.3%)

Steps

Iters	Range		Point
9	-2.951990989665665e-304	3.707064043527614e-307	-1.85078885647426e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-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	24	25
2	32	25
3	37	25
4	39	25
5	39	25

end138.0ms (3%)

Compiler: Compiled 173 to 129 computations (25.4% saved)

Details

analyze4.0ms (0.1%)

sample694.0ms (14.9%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite38.0ms (0.8%)

simplify12.0ms (0.2%)

prune34.0ms (0.7%)

localize12.0ms (0.3%)

series804.0ms (17.3%)

rewrite81.0ms (1.7%)

simplify132.0ms (2.8%)

prune104.0ms (2.2%)

localize11.0ms (0.2%)

series951.0ms (20.4%)

rewrite63.0ms (1.4%)

simplify117.0ms (2.5%)

prune98.0ms (2.1%)

localize13.0ms (0.3%)

series964.0ms (20.7%)

rewrite42.0ms (0.9%)

simplify139.0ms (3%)

prune94.0ms (2%)

regimes82.0ms (1.8%)

bsearch15.0ms (0.3%)

simplify3.0ms (0.1%)

end138.0ms (3%)

Profiling