Details

analyze31.0ms (0.8%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample922.0ms (24.6%)

Infinites

0% of outputs are infinite.

Results

466.0ms	6461×	body	128	valid
140.0ms	648×	body	1024	valid
108.0ms	680×	body	512	valid
60.0ms	458×	body	256	valid
2.0ms	9×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify201.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

1996×	`fma-def_binary64`
1626×	`fma-neg_binary64`
1098×	`div-sub_binary64`
733×	`sub-neg_binary64`
664×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	43	16
3	102	14
4	274	14
5	652	14
6	1272	14
7	1697	14
8	2416	14
9	2933	14
10	3278	14
11	3461	14
12	1980	14
13	1996	14
14	2659	14
15	2539	14
16	2497	14
17	2531	14
18	2531	14
19	4723	14
20	4903	14
21	5942	14

prune5.0ms (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

13.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	20.3b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	13.4b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series25.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
8.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

2 → 57

Calls

2 calls:

5.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
0.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

simplify84.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
491×	`associate--l+_binary64`
425×	`associate--r+_binary64`
390×	`associate-+l+_binary64`
315×	`fma-def_binary64`

Counts

105 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2086
1	416	1897
2	1275	1850
3	4701	1850
4	5402	1850

prune82.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	100	4	104

Error

0.0b

Counts

104 → 4

Alt Table

Status	Error	Program
	38.4b	(/.f64 (*.f64 y x) (+.f64 1 y))
▶	33.3b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
✓	13.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	37.0b	(log.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

Compiler

Compiled 1914 to 1312 computations (31.5% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.7b	(/.f64 x (*.f64 y y))
✓	6.7b	(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	8.4b	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
✓	10.6b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))

series157.0ms (4.2%)

Counts

4 → 96

Calls

4 calls:

64.0ms	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
34.0ms	(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
33.0ms	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
25.0ms	(/.f64 x (*.f64 y y))

rewrite137.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`*-un-lft-identity_binary64`
158×	`distribute-lft-out_binary64`
57×	`times-frac_binary64`
51×	`div-inv_binary64`
50×	`add-log-exp_binary64`

Counts

4 → 237

Calls

4 calls:

44.0ms	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
27.0ms	(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
15.0ms	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
3.0ms	(/.f64 x (*.f64 y y))

simplify222.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

487×	`distribute-rgt-in_binary64`
478×	`associate-l_binary64`
467×	`distribute-lft-in_binary64`
224×	`fma-def_binary64`
103×	`sub-neg_binary64`

Counts

333 → 258

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	338	18732
1	1193	13212
2	5025	13212

prune304.0ms (8.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	257	5	262

Error

0.0b

Counts

262 → 5

Alt Table

Status	Error	Program
	56.8b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (/.f64 (fma.f64 (pow.f64 y 3) (-.f64 (/.f64 (/.f64 1 (pow.f64 y 3)) y) (.f64 (/.f64 (+.f64 x -1) y) (/.f64 (+.f64 x -1) y))) (.f64 x (-.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))) (.f64 (pow.f64 y 3) (-.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))))
✓	13.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	38.4b	(/.f64 (*.f64 y x) (+.f64 1 y))
✓	33.3b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
▶	37.0b	(log.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

Compiler

Compiled 16044 to 8306 computations (48.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))
	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	4.3b	(log.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
	13.4b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series25.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))
11.0ms	(log.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`exp-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`log-prod_binary64`

Counts

2 → 32

Calls

2 calls:

1.0ms	(log.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
1.0ms	(exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))

simplify76.0ms (2%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-def_binary64`
705×	`times-frac_binary64`
209×	`cancel-sign-sub-inv_binary64`
183×	`fma-neg_binary64`
167×	`sub-neg_binary64`

Counts

80 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	2117
1	525	2023
2	1887	1935
3	4910	1935
4	5006	1935

prune128.0ms (3.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	202	5	207

Error

0.0b

Counts

207 → 5

Alt Table

Status	Error	Program
	56.8b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (/.f64 (fma.f64 (pow.f64 y 3) (-.f64 (/.f64 (/.f64 1 (pow.f64 y 3)) y) (.f64 (/.f64 (+.f64 x -1) y) (/.f64 (+.f64 x -1) y))) (.f64 x (-.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))) (.f64 (pow.f64 y 3) (-.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))))
✓	13.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
▶	38.4b	(/.f64 (*.f64 y x) (+.f64 1 y))
✓	33.3b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
✓	37.0b	(log.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

Compiler

Compiled 4500 to 3153 computations (29.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.1b	(/.f64 (*.f64 y x) (+.f64 1 y))

series9.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(/.f64 (*.f64 y x) (+.f64 1 y))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`associate-/r*_binary64`
4×	`times-frac_binary64`

Counts

1 → 27

Calls

1 calls:

5.0ms

(/.f64 (*.f64 y x) (+.f64 1 y))

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-neg_binary64`
674×	`fma-def_binary64`
649×	`times-frac_binary64`
451×	`associate-/l*_binary64`
257×	`cancel-sign-sub-inv_binary64`

Counts

39 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	79	551
1	217	478
2	695	473
3	2903	473
4	4647	473
5	4981	473

prune38.0ms (1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	57	5	62

Error

0.0b

Counts

62 → 5

Alt Table

Status	Error	Program
	56.8b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (/.f64 (fma.f64 (pow.f64 y 3) (-.f64 (/.f64 (/.f64 1 (pow.f64 y 3)) y) (.f64 (/.f64 (+.f64 x -1) y) (/.f64 (+.f64 x -1) y))) (.f64 x (-.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))) (.f64 (pow.f64 y 3) (-.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))))
✓	13.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
✓	38.4b	(/.f64 (*.f64 y x) (+.f64 1 y))
✓	33.3b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
✓	37.0b	(log.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

Compiler

Compiled 850 to 487 computations (42.7% saved)

regimes1.0s (27.5%)

Accuracy

Total 0.1b remaining (72.7%)

Threshold costs 0.1b (72.7%)

Counts

116 → 3

Compiler

Compiled 14704 to 9453 computations (35.7% saved)

bsearch33.0ms (0.9%)

Steps

Iters	Range		Point
9	0.0001530763031767488	199499.97938113092	180128.4190764583
9	-46359351.18093939	-9.054875420327296	-12257.264768591502

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
13×	`sub-neg_binary64`
10×	`distribute-neg-in_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	106
1	46	106
2	64	106
3	90	106
4	113	106
5	126	106
6	131	106
7	132	106
8	128	106

end118.0ms (3.2%)

Compiler: Compiled 284 to 181 computations (36.3% saved)

Details

analyze31.0ms (0.8%)

sample922.0ms (24.6%)

simplify201.0ms (5.4%)

prune5.0ms (0.1%)

localize6.0ms (0.2%)

series25.0ms (0.7%)

rewrite9.0ms (0.2%)

simplify84.0ms (2.2%)

prune82.0ms (2.2%)

localize15.0ms (0.4%)

series157.0ms (4.2%)

rewrite137.0ms (3.6%)

simplify222.0ms (5.9%)

prune304.0ms (8.1%)

localize9.0ms (0.2%)

series25.0ms (0.7%)

rewrite4.0ms (0.1%)

simplify76.0ms (2%)

prune128.0ms (3.4%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite6.0ms (0.2%)

simplify64.0ms (1.7%)

prune38.0ms (1%)

regimes1.0s (27.5%)

bsearch33.0ms (0.9%)

simplify7.0ms (0.2%)

end118.0ms (3.2%)

Profiling