Details

analyze177.0ms (6.2%)

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
25%	74.9%	0.1%	4
31.2%	68.6%	0.1%	5
43.7%	56.2%	0.1%	6
53%	46.8%	0.1%	7
59.3%	40.6%	0.1%	8
67.9%	32%	0.1%	9
75.5%	24.4%	0.1%	10
79.5%	20.4%	0.1%	11
84%	15.8%	0.1%	12
87.5%	12.4%	0.1%	13
89.7%	10.2%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample903.0ms (31.5%)

Infinites

0% of outputs are infinite.

Results

756.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify141.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

2495×	`fma-neg_binary64`
1241×	`fma-def_binary64`
1051×	`div-sub_binary64`
520×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	20	18
2	31	18
3	48	18
4	71	18
5	103	18
6	155	18
7	209	18
8	270	18
9	300	16
10	389	16
11	599	16
12	934	16
13	1583	16
14	1525	16
15	1839	16
16	1745	16
17	1773	16
18	1933	16
19	2758	16
20	3102	16
21	4012	16
22	4885	16
23	4851	16

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	3.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 84 to 56 computations (33.3% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	0.0b	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
✓	0.0b	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
✓	0.3b	(/.f64 -5641895835477563/5000000000000000 y)

series111.0ms (3.9%)

Counts

4 → 108

Calls

4 calls:

50.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
47.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
12.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
2.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
2.0ms	(/.f64 -5641895835477563/5000000000000000 y)
2.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
0.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)

simplify103.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

759×	`associate-/l*_binary64`
549×	`fma-def_binary64`
209×	`distribute-rgt-in_binary64`
152×	`associate-/l/_binary64`
149×	`distribute-lft-in_binary64`

Counts

193 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	4154
1	654	3971
2	1995	3895
3	5228	3895

prune143.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	157	6	163

Error

Counts

163 → 6

Alt Table

Status	Error	Program
	10.8b	(+.f64 x (expm1.f64 (log1p.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))
	23.7b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	11.9b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
▶	3.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
	34.0b	(+.f64 x (/.f64 -1 (exp.f64 (log.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))

Compiler

Compiled 3861 to 2423 computations (37.2% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	1.6b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	5.7b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series91.0ms (3.2%)

Counts

4 → 112

Calls

4 calls:

40.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
39.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
10.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
2.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 84

Calls

4 calls:

7.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
5.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
5.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
3.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

simplify139.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary64`
270×	`fma-neg_binary64`
253×	`associate-/r/_binary64`
229×	`cancel-sign-sub-inv_binary64`
155×	`associate-/l/_binary64`

Counts

196 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	4366
1	671	4279
2	2246	4156
3	4858	4146
4	4953	4146

prune167.0ms (5.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	208	6	214

Error

Counts

214 → 6

Alt Table

Status	Error	Program
▶	10.8b	(+.f64 x (expm1.f64 (log1p.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))
	23.7b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	11.9b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
✓	3.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
	34.0b	(+.f64 x (/.f64 -1 (exp.f64 (log.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))

Compiler

Compiled 4889 to 2533 computations (48.2% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
	0.0b	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
	0.3b	(/.f64 -5641895835477563/5000000000000000 y)
✓	0.8b	(expm1.f64 (log1p.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))))

series45.0ms (1.6%)

Counts

1 → 36

Calls

1 calls:

45.0ms

(expm1.f64 (log1p.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))))

simplify67.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-/l*_binary64`
630×	`associate-/r*_binary64`
327×	`fma-def_binary64`
242×	`associate-*l/_binary64`
130×	`distribute-rgt-in_binary64`

Counts

47 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1430
1	342	1395
2	1319	1332
3	5000	1324
4	5027	1324

prune129.0ms (4.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	156	6	162

Error

Counts

162 → 6

Alt Table

Status	Error	Program
✓	10.8b	(+.f64 x (expm1.f64 (log1p.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))
	23.7b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	11.9b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
✓	3.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
	34.0b	(+.f64 x (/.f64 -1 (exp.f64 (log.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))

Compiler

Compiled 3964 to 2605 computations (34.3% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
✓	0.0b	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))
✓	0.1b	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y))))
✓	0.3b	(*.f64 5641895835477563/5000000000000000 (/.f64 1 y))

series28.0ms (1%)

Counts

4 → 66

Calls

4 calls:

11.0ms	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
11.0ms	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y))))
5.0ms	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))
2.0ms	(*.f64 5641895835477563/5000000000000000 (/.f64 1 y))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 106

Calls

4 calls:

6.0ms	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
5.0ms	(*.f64 5641895835477563/5000000000000000 (/.f64 1 y))
4.0ms	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y))))
3.0ms	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))

simplify104.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
538×	`fma-def_binary64`
450×	`associate-l_binary64`
418×	`associate-r_binary64`
204×	`associate-/r*_binary64`

Counts

172 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	2495
1	505	2363
2	1257	2326
3	4593	2326
4	5106	2326

prune163.0ms (5.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	1	2
Picked	0	1	1
Done	0	3	3
Total	205	6	211

Error

Counts

211 → 6

Alt Table

Status	Error	Program
✓	10.8b	(+.f64 x (expm1.f64 (log1p.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))
	23.7b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
	18.6b	(+.f64 x (/.f64 -1 (cbrt.f64 (pow.f64 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y)) 3))))
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	11.9b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
✓	3.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 3806 to 2765 computations (27.4% saved)

regimes167.0ms (5.8%)

Accuracy

Total 0.0b remaining (91.3%)

Threshold costs 0.0b (91.3%)

Counts

32 → 1

Compiler

Compiled 2550 to 1869 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	12	16
2	12	16

end84.0ms (2.9%)

Compiler: Compiled 112 to 82 computations (26.8% saved)

Details

analyze177.0ms (6.2%)

sample903.0ms (31.5%)

simplify141.0ms (4.9%)

prune4.0ms (0.1%)

localize7.0ms (0.3%)

series111.0ms (3.9%)

rewrite12.0ms (0.4%)

simplify103.0ms (3.6%)

prune143.0ms (5%)

localize15.0ms (0.5%)

series91.0ms (3.2%)

rewrite23.0ms (0.8%)

simplify139.0ms (4.9%)

prune167.0ms (5.8%)

localize10.0ms (0.4%)

series45.0ms (1.6%)

rewrite1.0ms (0%)

simplify67.0ms (2.3%)

prune129.0ms (4.5%)

localize6.0ms (0.2%)

series28.0ms (1%)

rewrite23.0ms (0.8%)

simplify104.0ms (3.6%)

prune163.0ms (5.7%)

regimes167.0ms (5.8%)

simplify3.0ms (0.1%)

end84.0ms (2.9%)

Profiling