Details

analyze373.0ms (8.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
9.4%	65.5%	25.1%	8
14%	35.9%	50.1%	9
21.1%	28.9%	50.1%	10
24.6%	25.4%	50.1%	11
28.7%	21.3%	50.1%	12
33.4%	16.5%	50.1%	13
35.8%	14.1%	50.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (26.9%)

Results

1.1s	8254×	body	128	valid
4.0ms	38×	body	128	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify132.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
610×	`unsub-neg_binary64`
567×	`distribute-rgt-in_binary64`
442×	`sub-neg_binary64`
412×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	25	18
2	75	16
3	253	16
4	654	16
5	1767	16
6	2167	16
7	2284	16
8	2375	16
9	2374	16
10	2391	16
11	2701	16
12	3417	16
13	4877	16
14	4713	16
15	4967	16

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))

Compiler

Compiled 54 to 33 computations (38.9% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
✓	0.1b	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

series120.0ms (2.6%)

Counts

2 → 60

Calls

2 calls:

78.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
41.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
19×	`add-cube-cbrt_binary64`
14×	`associate--r+_binary64`

Counts

2 → 65

Calls

2 calls:

13.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
0.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

simplify95.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-def_binary64`
547×	`distribute-rgt-in_binary64`
508×	`distribute-lft-in_binary64`
456×	`fma-neg_binary64`
232×	`exp-sum_binary64`

Counts

125 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2510
1	373	2200
2	1256	1943
3	4472	1943
4	5111	1943

prune127.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Error

0.0b

Counts

126 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
	0.9b	(-.f64 y (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
	26.6b	(*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (-.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	44.3b	(/.f64 (-.f64 (pow.f64 y 3) (pow.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) 3)) (+.f64 (.f64 y y) (+.f64 (.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (*.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))))

Compiler

Compiled 3253 to 1644 computations (49.5% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
✓	0.1b	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

series89.0ms (2%)

Counts

2 → 48

Calls

2 calls:

81.0ms	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
8.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate--r+_binary64`

Counts

2 → 65

Calls

2 calls:

9.0ms	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
0.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

simplify83.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary64`
608×	`fma-neg_binary64`
469×	`associate-l_binary64`
402×	`associate-r_binary64`
352×	`distribute-rgt-in_binary64`

Counts

113 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2157
1	375	1915
2	1163	1750
3	4304	1750
4	4929	1750

prune91.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	109	5	114

Error

0.0b

Counts

114 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
	0.9b	(-.f64 y (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
▶	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
	26.6b	(*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (-.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	44.3b	(/.f64 (-.f64 (pow.f64 y 3) (pow.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) 3)) (+.f64 (.f64 y y) (+.f64 (.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (*.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))))

Compiler

Compiled 2701 to 1122 computations (58.5% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
✓	0.3b	(*.f64 y (log.f64 y))

series201.0ms (4.4%)

Counts

2 → 44

Calls

2 calls:

169.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
32.0ms	(*.f64 y (log.f64 y))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
30×	`prod-diff_binary64`
25×	`add-cube-cbrt_binary64`
17×	`associate--r+_binary64`

Counts

2 → 92

Calls

2 calls:

9.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
6.0ms	(*.f64 y (log.f64 y))

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

792×	`fma-def_binary64`
607×	`distribute-rgt-in_binary64`
557×	`distribute-lft-in_binary64`
470×	`fma-neg_binary64`
186×	`cancel-sign-sub-inv_binary64`

Counts

136 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	2348
1	411	2065
2	1422	1994
3	4826	1994
4	4962	1994

prune117.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	130	4	134

Error

0.0b

Counts

134 → 4

Alt Table

Status	Error	Program
	0.2b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (log.f64 y))) (*.f64 1/2 (log.f64 y)))) x))
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
▶	0.1b	(fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (-.f64 x (fma.f64 (log.f64 y) (+.f64 y 1/2) z)))
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (+.f64 (.f64 y (.f64 2 (log.f64 (cbrt.f64 y)))) (.f64 y (log.f64 (cbrt.f64 y)))) (.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 3891 to 1743 computations (55.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (-.f64 x (fma.f64 (log.f64 y) (+.f64 y 1/2) z)))
✓	0.1b	(fma.f64 (log.f64 y) (+.f64 y 1/2) z)
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)

series418.0ms (9.3%)

Counts

4 → 84

Calls

4 calls:

303.0ms	(fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (-.f64 x (fma.f64 (log.f64 y) (+.f64 y 1/2) z)))
47.0ms	(fma.f64 (log.f64 y) (+.f64 y 1/2) z)
36.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
32.0ms	(cbrt.f64 y)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 75

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
0.0ms	(fma.f64 (log.f64 y) (+.f64 y 1/2) z)
0.0ms	(fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (-.f64 x (fma.f64 (log.f64 y) (+.f64 y 1/2) z)))

simplify95.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
432×	`fma-def_binary64`
308×	`distribute-rgt-in_binary64`
307×	`sub-neg_binary64`
274×	`distribute-lft-in_binary64`

Counts

159 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	1777
1	276	1623
2	974	1565
3	3292	1548
4	4558	1548
5	4956	1548

prune175.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	172	4	176

Error

0.0b

Counts

176 → 4

Alt Table

Status	Error	Program
	0.2b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (log.f64 y))) (*.f64 1/2 (log.f64 y)))) x))
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
✓	0.1b	(fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (-.f64 x (fma.f64 (log.f64 y) (+.f64 y 1/2) z)))
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (+.f64 (.f64 y (.f64 2 (log.f64 (cbrt.f64 y)))) (.f64 y (log.f64 (cbrt.f64 y)))) (.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 3590 to 1393 computations (61.2% saved)

regimes907.0ms (20.1%)

Accuracy

Total 0.1b remaining (70.6%)

Threshold costs 0.1b (70.6%)

Counts

166 → 1

Compiler

Compiled 16942 to 10593 computations (37.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
7×	`+-commutative_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	16	16
2	30	16
3	45	16
4	58	16
5	61	16
6	57	16

end79.0ms (1.8%)

Compiler: Compiled 111 to 68 computations (38.7% saved)

Details

analyze373.0ms (8.2%)

sample1.2s (26.9%)

simplify132.0ms (2.9%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series120.0ms (2.6%)

rewrite19.0ms (0.4%)

simplify95.0ms (2.1%)

prune127.0ms (2.8%)

localize8.0ms (0.2%)

series89.0ms (2%)

rewrite15.0ms (0.3%)

simplify83.0ms (1.8%)

prune91.0ms (2%)

localize9.0ms (0.2%)

series201.0ms (4.4%)

rewrite23.0ms (0.5%)

simplify98.0ms (2.2%)

prune117.0ms (2.6%)

localize11.0ms (0.2%)

series418.0ms (9.3%)

rewrite8.0ms (0.2%)

simplify95.0ms (2.1%)

prune175.0ms (3.9%)

regimes907.0ms (20.1%)

simplify3.0ms (0.1%)

end79.0ms (1.8%)

Profiling