Details

analyze270.0ms (9%)

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
25%	74.9%	0.1%	5
37.4%	62.4%	0.1%	6
46.8%	53%	0.1%	7
52.3%	47.6%	0.1%	8
65.5%	34.3%	0.1%	9
71%	28.9%	0.1%	10
75%	24.9%	0.1%	11
81.6%	18.2%	0.1%	12
84.5%	15.4%	0.1%	13
86.9%	13%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample136.0ms (4.6%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify138.0ms (4.6%)

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

prune3.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	2.1b	(+.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 (0.2%)

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)))
✓	0.1b	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
✓	0.2b	(/.f64 -5641895835477563/5000000000000000 y)
✓	0.2b	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)

series111.0ms (3.7%)

Counts

4 → 108

Calls

4 calls:

50.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
47.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
13.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
1.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite45.0ms (1.5%)

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:

35.0ms	(/.f64 -5641895835477563/5000000000000000 y)
4.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
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)

simplify111.0ms (3.7%)

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

prune127.0ms (4.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	159	4	163

Error

0.2b

Counts

163 → 4

Alt Table

Status	Error	Program
	27.9b	(/.f64 (fma.f64 x x (/.f64 -1 (*.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))) (+.f64 x (/.f64 1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))))
	22.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
▶	1.2b	(fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	2.1b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 3865 to 2409 computations (37.7% saved)

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 -5641895835477563/5000000000000000 y)
	0.2b	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)

series71.0ms (2.4%)

Counts

2 → 24

Calls

2 calls:

36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
34.0ms	(cbrt.f64 x)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 55

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify64.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune111.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	167	5	172

Error

0.2b

Counts

172 → 5

Alt Table

Status	Error	Program
	27.9b	(/.f64 (fma.f64 x x (/.f64 -1 (*.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))) (+.f64 x (/.f64 1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))))
	22.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	1.2b	(fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	34.7b	(fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (pow.f64 (*.f64 -1 x) 1/3) (cbrt.f64 -1)) (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	2.1b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 3795 to 1659 computations (56.3% saved)

localize8.0ms (0.3%)

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))
✓	0.4b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	6.5b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series104.0ms (3.5%)

Counts

4 → 112

Calls

4 calls:

47.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
43.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
11.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
2.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite25.0ms (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:

9.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
6.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
4.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
3.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

simplify167.0ms (5.6%)

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

prune174.0ms (5.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	208	5	213

Error

0.2b

Counts

213 → 5

Alt Table

Status	Error	Program
	31.9b	(+.f64 x (.f64 (/.f64 y (-.f64 (.f64 (pow.f64 (exp.f64 z) 2) 31830988618379068626528276418969/25000000000000000000000000000000) (.f64 y (.f64 y (.f64 x x))))) (+.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y))))
▶	22.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	1.2b	(fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	34.7b	(fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (pow.f64 (*.f64 -1 x) 1/3) (cbrt.f64 -1)) (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	2.1b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 4915 to 2541 computations (48.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.2b	(/.f64 y (exp.f64 z))

series36.0ms (1.2%)

Counts

2 → 40

Calls

2 calls:

21.0ms	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
14.0ms	(/.f64 y (exp.f64 z))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

3.0ms	(/.f64 y (exp.f64 z))
0.0ms	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

simplify88.0ms (3%)

Algorithm

1×	egg-herbie

Rules

667×	`cancel-sign-sub-inv_binary64`
491×	`div-sub_binary64`
379×	`associate-/l*_binary64`
372×	`fma-neg_binary64`
357×	`sub-neg_binary64`

Counts

79 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	940
1	212	889
2	532	882
3	1512	871
4	4180	871
5	4619	871
6	5253	871

prune39.0ms (1.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	61	5	66

Error

0.2b

Counts

66 → 5

Alt Table

Status	Error	Program
	31.9b	(+.f64 x (.f64 (/.f64 y (-.f64 (.f64 (pow.f64 (exp.f64 z) 2) 31830988618379068626528276418969/25000000000000000000000000000000) (.f64 y (.f64 y (.f64 x x))))) (+.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y))))
✓	22.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	1.2b	(fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	34.7b	(fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (pow.f64 (*.f64 -1 x) 1/3) (cbrt.f64 -1)) (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	2.1b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 870 to 410 computations (52.9% saved)

regimes395.0ms (13.2%)

Accuracy

Total 0.1b remaining (84.8%)

Threshold costs 0.1b (84.8%)

Counts

64 → 1

Compiler

Compiled 6177 to 4259 computations (31.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	25	18
2	37	18
3	45	18
4	51	18
5	54	18
6	55	18
7	52	18

end1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample720.0ms (24.1%)

Algorithm

1×

intervals

Results

389.0ms

8000×

body

128

valid

Compiler

Compiled 135 to 92 computations (31.9% saved)

Details

analyze270.0ms (9%)

sample136.0ms (4.6%)

simplify138.0ms (4.6%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series111.0ms (3.7%)

rewrite45.0ms (1.5%)

simplify111.0ms (3.7%)

prune127.0ms (4.3%)

localize18.0ms (0.6%)

series71.0ms (2.4%)

rewrite7.0ms (0.2%)

simplify64.0ms (2.1%)

prune111.0ms (3.7%)

localize8.0ms (0.3%)

series104.0ms (3.5%)

rewrite25.0ms (0.8%)

simplify167.0ms (5.6%)

prune174.0ms (5.8%)

localize5.0ms (0.2%)

series36.0ms (1.2%)

rewrite5.0ms (0.2%)

simplify88.0ms (3%)

prune39.0ms (1.3%)

regimes395.0ms (13.2%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample720.0ms (24.1%)

Profiling