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)

sample681.0ms (16.9%)

Results

653.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify7.0ms (0.2%)

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

35.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	33.6b	(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 (1%)

Algorithm

1×	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:

40.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

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

simplify11.0ms (0.3%)

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

prune40.0ms (1%)

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
	15.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	33.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.5b	(*.f64 (sqrt.f64 2) x)
✓	35.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	43.2b	(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 (sqrt.f64 x) (+.f64 x x)) 1/2))
▶	15.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))

Compiler

Compiled 794 to 525 computations (33.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
✓	0.6b	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
✓	0.6b	(cbrt.f64 (+.f64 x x))
✓	15.1b	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)

series1.0s (25%)

Counts

4 → 48

Calls

4 calls:

897.0ms	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)
47.0ms	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
35.0ms	(cbrt.f64 (+.f64 x x))
27.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))

rewrite62.0ms (1.5%)

Algorithm

1×	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:

59.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
59.0ms	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
59.0ms	(cbrt.f64 (+.f64 x x))
59.0ms	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)

Iterations

Useful iterations: 1 (0.0ms)

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

simplify121.0ms (3%)

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

prune99.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	230	11	241

Error

0.1b

Counts

241 → 11

Alt Table

Status	Error	Program
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	15.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2))
▶	15.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	33.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.5b	(*.f64 (sqrt.f64 2) x)
✓	35.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	41.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (exp.f64 (*.f64 (log.f64 (+.f64 x x)) 1/3)) x) 1/2))
	16.0b	(.f64 (sqrt.f64 (pow.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) 2)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	43.2b	(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 (sqrt.f64 x) (+.f64 x x)) 1/2))
✓	15.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))

Compiler

Compiled 5061 to 2333 computations (53.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.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)
✓	15.0b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

series1.0s (25.1%)

Counts

4 → 48

Calls

4 calls:

924.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
39.0ms	(pow.f64 (cbrt.f64 x) 2)
30.0ms	(cbrt.f64 x)
16.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

rewrite63.0ms (1.6%)

Algorithm

1×	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 → 83

Calls

4 calls:

62.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
62.0ms	(pow.f64 (cbrt.f64 x) 2)
62.0ms	(cbrt.f64 x)
62.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	219	28
2	2178	28
3	5792	28

simplify136.0ms (3.4%)

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

131 → 95

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

prune65.0ms (1.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	124	11	135

Error

0.1b

Counts

135 → 11

Alt Table

Status	Error	Program
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	15.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2))
▶	15.7b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	33.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.5b	(*.f64 (sqrt.f64 2) 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)))
✓	35.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	41.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (exp.f64 (*.f64 (log.f64 (+.f64 x x)) 1/3)) x) 1/2))
	16.0b	(.f64 (sqrt.f64 (pow.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) 2)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
✓	15.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))

Compiler

Compiled 2277 to 1205 computations (47.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.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)
	15.0b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
✓	15.1b	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

series128.0ms (3.2%)

Counts

2 → 24

Calls

2 calls:

87.0ms	(.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)))

rewrite50.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

918×	`prod-diff_binary64`
832×	`expm1-log1p-u_binary64`
107×	`add-sqr-sqrt_binary64`
103×	`log1p-expm1-u_binary64`
99×	`add-cube-cbrt_binary64`

Counts

2 → 45

Calls

2 calls:

49.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
49.0ms	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	230	15
2	2236	15
3	5175	15

simplify119.0ms (3%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-def_binary64`
531×	`associate-l_binary64`
478×	`sqr-pow_binary64`
474×	`unswap-sqr_binary64`
289×	`associate-r_binary64`

Counts

69 → 52

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	288
1	47	288
2	92	288
3	174	288
4	385	288
5	1056	288
6	1695	288
7	2280	288
8	2955	288
9	3564	288
10	4112	288
11	4714	288
12	4996	288
13	4691	288

prune62.0ms (1.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	3	5	8
Picked	0	1	1
Done	0	2	2
Total	134	11	145

Error

0.1b

Counts

145 → 11

Alt Table

Status	Error	Program
	33.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	15.8b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	32.5b	(*.f64 (sqrt.f64 2) x)
	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 (cbrt.f64 x) (+.f64 x x)) 1/4)))
✓	15.7b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	28.8b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (expm1.f64 (log1p.f64 (cbrt.f64 x)))))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) 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)))
✓	35.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	15.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))

Compiler

Compiled 2438 to 1064 computations (56.4% saved)

regimes125.0ms (3.1%)

Accuracy

Total 0.3b remaining (79%)

Threshold costs 0.3b (79%)

Counts

35 → 2

Compiler

Compiled 1683 to 1145 computations (32% saved)

bsearch15.0ms (0.4%)

Steps

Iters	Range		Point
9	-5.0244719348910686e-303	1.998438837190896e-307	-1.04069420257774e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	10	20
1	19	20
2	27	20
3	32	20
4	34	20
5	34	20

end128.0ms (3.2%)

Compiler: Compiled 181 to 119 computations (34.3% saved)

Details

analyze4.0ms (0.1%)

sample681.0ms (16.9%)

simplify7.0ms (0.2%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite41.0ms (1%)

simplify11.0ms (0.3%)

prune40.0ms (1%)

localize11.0ms (0.3%)

series1.0s (25%)

rewrite62.0ms (1.5%)

simplify121.0ms (3%)

prune99.0ms (2.5%)

localize10.0ms (0.3%)

series1.0s (25.1%)

rewrite63.0ms (1.6%)

simplify136.0ms (3.4%)

prune65.0ms (1.6%)

localize11.0ms (0.3%)

series128.0ms (3.2%)

rewrite50.0ms (1.2%)

simplify119.0ms (3%)

prune62.0ms (1.5%)

regimes125.0ms (3.1%)

bsearch15.0ms (0.4%)

simplify6.0ms (0.2%)

end128.0ms (3.2%)

Profiling