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 (20.7%)

Results

654.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.2%)

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

29.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.2b	(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
✓	28.2b	(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))

rewrite31.0ms (0.9%)

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:

30.0ms

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

simplify10.0ms (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`

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

prune35.0ms (1.1%)

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
✓	29.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
▶	15.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	31.0b	(*.f64 (sqrt.f64 2) x)
	31.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	32.3b	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3))
	29.5b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 x x) 4))) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	41.0b	(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 (sqrt.f64 x) (+.f64 x x)) 1/2))
	31.7b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	32.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 830 to 589 computations (29% saved)

localize12.0ms (0.4%)

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)
✓	14.7b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

series782.0ms (23.7%)

Counts

4 → 48

Calls

4 calls:

699.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
38.0ms	(pow.f64 (cbrt.f64 x) 2)
28.0ms	(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))

rewrite47.0ms (1.4%)

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:

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

simplify77.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
488×	`sqr-pow_binary64`
412×	`unswap-sqr_binary64`
322×	`*-commutative_binary64`
207×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	400
1	53	400
2	103	400
3	257	400
4	930	400
5	1817	400
6	1992	400
7	2230	400
8	2599	400
9	3114	400
10	3594	400
11	4218	400
12	4947	400

Stop Event

1×	node limit

Counts

128 → 93

prune70.0ms (2.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	117	14	131

Error

0.1b

Counts

131 → 14

Alt Table

Status	Error	Program
	31.7b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	15.9b	(.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))
	15.4b	(.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)))
	31.0b	(*.f64 (sqrt.f64 2) x)
	15.4b	(.f64 (sqrt.f64 (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 x (cbrt.f64 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	31.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	15.3b	(.f64 (sqrt.f64 (pow.f64 (fabs.f64 (cbrt.f64 x)) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	32.3b	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3))
✓	29.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	29.5b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 x x) 4))) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	41.0b	(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 (sqrt.f64 x) (+.f64 x x)) 1/2))
▶	15.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	32.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	15.4b	(.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (.f64 x (cbrt.f64 x))))) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

Compiler

Compiled 2388 to 1289 computations (46% 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)
	14.7b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
✓	14.7b	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

series132.0ms (4%)

Counts

2 → 24

Calls

2 calls:

81.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
51.0ms	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

rewrite45.0ms (1.4%)

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:

44.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
44.0ms	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

simplify47.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-def_binary64`
514×	`associate-l_binary64`
474×	`unswap-sqr_binary64`
306×	`associate-r_binary64`
225×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	288
1	47	288
2	95	288
3	197	288
4	512	288
5	1699	288
6	3056	288
7	3940	288
8	4818	288

Stop Event

1×	node limit

Counts

68 → 51

prune93.0ms (2.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	135	12	147

Error

0.1b

Counts

147 → 12

Alt Table

Status	Error	Program
▶	15.2b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 x (cbrt.f64 x)))))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	31.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	31.7b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	15.4b	(.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)))
	31.0b	(*.f64 (sqrt.f64 2) x)
	15.3b	(.f64 (sqrt.f64 (pow.f64 (fabs.f64 (cbrt.f64 x)) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	32.3b	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3))
✓	29.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	29.5b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 x x) 4))) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	41.0b	(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 (sqrt.f64 x) (+.f64 x x)) 1/2))
	32.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	15.5b	(.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))

Compiler

Compiled 2606 to 1190 computations (54.3% saved)

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) 2)
	0.6b	(cbrt.f64 x)
	14.7b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
✓	15.1b	(cbrt.f64 (*.f64 x (cbrt.f64 x)))

series583.0ms (17.7%)

Counts

2 → 24

Calls

2 calls:

297.0ms	(pow.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) 2)
286.0ms	(cbrt.f64 (*.f64 x (cbrt.f64 x)))

rewrite43.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

479×	`log1p-expm1-u_binary64`
479×	`expm1-log1p-u_binary64`
427×	`unpow-prod-down_binary64`
266×	`log-prod_binary64`
141×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	138	19
2	1503	19

Stop Event

1×	node limit

Counts

2 → 109

Calls

2 calls:

41.0ms	(pow.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) 2)
41.0ms	(cbrt.f64 (*.f64 x (cbrt.f64 x)))

simplify50.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

596×	`unswap-sqr_binary64`
333×	`sqr-pow_binary64`
259×	`associate-l_binary64`
230×	`*-commutative_binary64`
200×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	464
1	43	464
2	99	464
3	270	464
4	1057	316
5	2209	316
6	2405	316
7	2799	316
8	3513	316
9	4546	316

Stop Event

1×

unsound

Counts

133 → 117

prune169.0ms (5.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	285	12	297

Error

0.1b

Counts

297 → 12

Alt Table

Status	Error	Program
✓	15.2b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 x (cbrt.f64 x)))))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	31.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	31.7b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	15.4b	(.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)))
	31.0b	(*.f64 (sqrt.f64 2) x)
	15.3b	(.f64 (sqrt.f64 (pow.f64 (fabs.f64 (cbrt.f64 x)) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	32.3b	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3))
✓	29.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	29.5b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 x x) 4))) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	41.0b	(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 (sqrt.f64 x) (+.f64 x x)) 1/2))
	32.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	15.5b	(.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))

Compiler

Compiled 8959 to 3804 computations (57.5% saved)

regimes175.0ms (5.3%)

Accuracy

Total 0.3b remaining (76.7%)

Threshold costs 0.3b (76.7%)

Counts

51 → 2

Compiler

Compiled 2649 to 1826 computations (31.1% saved)

bsearch15.0ms (0.5%)

Steps

Iters	Range		Point
9	-4.119570298792794e-307	3.785377296366127e-303	-7.652228493472e-311

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.2%)

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 (4.4%)

Compiler: Compiled 201 to 138 computations (31.3% saved)

Details

analyze4.0ms (0.1%)

sample681.0ms (20.7%)

simplify6.0ms (0.2%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite31.0ms (0.9%)

simplify10.0ms (0.3%)

prune35.0ms (1.1%)

localize12.0ms (0.4%)

series782.0ms (23.7%)

rewrite47.0ms (1.4%)

simplify77.0ms (2.3%)

prune70.0ms (2.1%)

localize11.0ms (0.3%)

series132.0ms (4%)

rewrite45.0ms (1.4%)

simplify47.0ms (1.4%)

prune93.0ms (2.8%)

localize18.0ms (0.6%)

series583.0ms (17.7%)

rewrite43.0ms (1.3%)

simplify50.0ms (1.5%)

prune169.0ms (5.1%)

regimes175.0ms (5.3%)

bsearch15.0ms (0.5%)

simplify5.0ms (0.2%)

end145.0ms (4.4%)

Profiling