Details

analyze337.0ms (8.8%)

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)

sample1.6s (41.2%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify258.0ms (6.7%)

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

prune12.0ms (0.3%)

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)))
	1.6b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 84 to 56 computations (33.3% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(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)

series76.0ms (2%)

Counts

3 → 72

Calls

3 calls:

53.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
20.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
3.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 68

Calls

3 calls:

4.0ms	(/.f64 -5641895835477563/5000000000000000 y)
4.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
1.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)

simplify117.0ms (3%)

Algorithm

1×	egg-herbie

Rules

749×	`associate-/l*_binary64`
676×	`associate-/r*_binary64`
402×	`fma-def_binary64`
166×	`distribute-rgt-in_binary64`
153×	`associate-/l/_binary64`

Counts

140 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	2754
1	529	2581
2	1700	2532
3	5475	2532

prune212.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	114	3	117

Error

Counts

117 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	22.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
▶	1.6b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 2501 to 1575 computations (37% saved)

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	0.6b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	5.4b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series103.0ms (2.7%)

Counts

3 → 76

Calls

3 calls:

78.0ms

(/.f64 y (-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y)))

22.0ms

(-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y))

3.0ms

(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

6.0ms

(/.f64 y (-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y)))

5.0ms

(-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y))

4.0ms

(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

simplify118.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

649×	`associate-/r*_binary64`
641×	`fma-def_binary64`
252×	`associate-/r/_binary64`
154×	`associate-/l/_binary64`
129×	`cancel-sign-sub-inv_binary64`

Counts

143 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2944
1	538	2840
2	1885	2761
3	5021	2761

prune242.0ms (6.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	155	3	158

Error

Counts

158 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	22.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	1.6b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 3423 to 1748 computations (48.9% saved)

localize22.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	0.2b	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))

series72.0ms (1.9%)

Counts

2 → 40

Calls

2 calls:

42.0ms	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
30.0ms	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`

Counts

2 → 50

Calls

2 calls:

11.0ms	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))
5.0ms	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))

simplify179.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-neg_binary64`
547×	`cancel-sign-sub-inv_binary64`
270×	`fma-def_binary64`
263×	`associate-/l/_binary64`
214×	`associate-l_binary64`

Counts

90 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1086
1	320	1049
2	863	1038
3	2368	1023
4	4432	1010
5	4988	1010

prune86.0ms (2.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	83	3	86

Error

Counts

86 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	22.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	1.6b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 1248 to 610 computations (51.1% saved)

regimes232.0ms (6%)

Accuracy

Total 0.0b remaining (77.5%)

Threshold costs 0.0b (77.5%)

Counts

23 → 1

Compiler

Compiled 1732 to 1251 computations (27.8% saved)

simplify4.0ms (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

end105.0ms (2.7%)

Compiler: Compiled 68 to 48 computations (29.4% saved)

Details

analyze337.0ms (8.8%)

sample1.6s (41.2%)

simplify258.0ms (6.7%)

prune12.0ms (0.3%)

localize11.0ms (0.3%)

series76.0ms (2%)

rewrite13.0ms (0.4%)

simplify117.0ms (3%)

prune212.0ms (5.5%)

localize16.0ms (0.4%)

series103.0ms (2.7%)

rewrite17.0ms (0.5%)

simplify118.0ms (3.1%)

prune242.0ms (6.3%)

localize22.0ms (0.6%)

series72.0ms (1.9%)

rewrite21.0ms (0.6%)

simplify179.0ms (4.7%)

prune86.0ms (2.3%)

regimes232.0ms (6%)

simplify4.0ms (0.1%)

end105.0ms (2.7%)

Profiling