Details

analyze1.6s (11.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
12.9%	79.1%	8%	12
15.8%	76.2%	8%	13
18.4%	73.6%	8%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample7.4s (50.9%)

Results

2.4s	1542×	body	8192	exit
1.9s	1844×	body	1024	valid
867.0ms	3905×	body	128	valid
705.0ms	1411×	body	512	valid
454.0ms	1565×	body	128	invalid
427.0ms	336×	body	2048	valid
245.0ms	760×	body	256	valid
105.0ms	189×	body	1024	invalid
93.0ms	228×	body	512	invalid
48.0ms	163×	body	256	invalid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify246.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

3540×	`fma-neg_binary64`
744×	`div-sub_binary64`
658×	`sub-neg_binary64`
627×	`fma-def_binary64`
613×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	23	18
2	48	17
3	86	17
4	177	14
5	318	14
6	465	14
7	536	14
8	618	14
9	723	14
10	1083	14
11	1710	14
12	1873	14
13	2250	14
14	2803	14
15	3186	14
16	3529	14
17	3735	14
18	3809	14
19	4125	14
20	4337	14
21	3179	14
22	3171	14
23	3183	14
24	3183	14
25	4223	14
26	7145	14

prune5.0ms (0%)

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

1.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.4b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (expm1.f64 z))
✓	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.8b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series833.0ms (5.7%)

Counts

3 → 84

Calls

3 calls:

609.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
216.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
8.0ms	(*.f64 y (expm1.f64 z))

rewrite49.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

732×	`expm1-log1p-u_binary64`
731×	`log1p-expm1-u_binary64`
213×	`prod-diff_binary64`
147×	`log1p-udef_binary64`
80×	`add-sqr-sqrt_binary64`

Counts

3 → 67

Calls

3 calls:

47.0ms	(*.f64 y (expm1.f64 z))
46.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
46.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	158	25
2	1918	25
3	5181	25
0	0	0
1	0	0

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

525×	`cancel-sign-sub-inv_binary64`
348×	`fma-neg_binary64`
346×	`sub-neg_binary64`
268×	`fma-def_binary64`
226×	`associate-+r+_binary64`

Counts

151 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	2462
1	871	2190
2	3335	2184
3	4960	2184
4	5096	2184

prune165.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	7	138

Error

0.0b

Counts

138 → 7

Alt Table

Status	Error	Program
	35.8b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (sqrt.f64 t))))
	16.4b	(-.f64 x (.f64 (/.f64 1 (cbrt.f64 (.f64 t t))) (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (cbrt.f64 t))))
	21.3b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 1 t))))
▶	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
✓	1.4b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	33.5b	(-.f64 x (-.f64 (+.f64 (.f64 (/.f64 y t) z) (fma.f64 1/2 (.f64 (/.f64 y t) (.f64 z z)) (fma.f64 1/2 (.f64 (/.f64 (pow.f64 y 3) t) (pow.f64 z 4)) (fma.f64 1/24 (.f64 (/.f64 y t) (pow.f64 z 4)) (fma.f64 1/3 (.f64 (/.f64 (pow.f64 y 3) t) (pow.f64 z 3)) (.f64 1/6 (.f64 (/.f64 y t) (pow.f64 z 3)))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 y y) t) (pow.f64 z 3)) (fma.f64 7/24 (.f64 (/.f64 (.f64 y y) t) (pow.f64 z 4)) (fma.f64 1/2 (.f64 (/.f64 (.f64 y y) t) (.f64 z z)) (.f64 1/4 (*.f64 (/.f64 (pow.f64 y 4) t) (pow.f64 z 4))))))))
	1.5b	(-.f64 x (pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1))

Compiler

Compiled 4114 to 2210 computations (46.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (expm1.f64 z))
	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.9b	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))

series582.0ms (4%)

Counts

1 → 36

Calls

1 calls:

582.0ms

(*.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (/.f64 1 t))

rewrite47.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

801×	`expm1-log1p-u_binary64`
800×	`log1p-expm1-u_binary64`
204×	`prod-diff_binary64`
94×	`add-sqr-sqrt_binary64`
85×	`add-cbrt-cube_binary64`

Counts

1 → 26

Calls

1 calls:

46.0ms

(*.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (/.f64 1 t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	194	11
2	2140	11
3	5315	11
0	0	0
1	0	0

simplify45.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

490×	`associate-/r*_binary64`
385×	`fma-def_binary64`
354×	`associate-/l*_binary64`
177×	`sub-neg_binary64`
168×	`distribute-rgt-in_binary64`

Counts

62 → 59

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	1375
1	575	1215
2	2020	1128
3	5079	1128

prune130.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	130	6	136

Error

0.0b

Counts

136 → 6

Alt Table

Status	Error	Program
	35.8b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	21.3b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
	32.2b	(-.f64 x (fma.f64 -1/2 (.f64 (.f64 (/.f64 y t) y) (+.f64 (.f64 z z) (pow.f64 z 3))) (fma.f64 1/3 (.f64 (/.f64 (pow.f64 y 3) t) (pow.f64 z 3)) (fma.f64 (/.f64 y t) z (fma.f64 1/2 (.f64 (/.f64 y t) (.f64 z z)) (.f64 1/6 (.f64 (/.f64 y t) (pow.f64 z 3))))))))
✓	1.4b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
▶	1.5b	(-.f64 x (pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1))

Compiler

Compiled 3864 to 2183 computations (43.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (expm1.f64 z))
	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.6b	(pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1)
✓	4.8b	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

series1.6s (11.2%)

Counts

2 → 72

Calls

2 calls:

846.0ms	(pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1)
779.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

rewrite56.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

880×	`expm1-log1p-u_binary64`
879×	`log1p-expm1-u_binary64`
213×	`prod-diff_binary64`
99×	`add-sqr-sqrt_binary64`
90×	`add-cbrt-cube_binary64`

Counts

2 → 77

Calls

2 calls:

55.0ms	(pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1)
55.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	200	22
2	2306	22
3	5775	22
0	0	0
1	0	0

simplify121.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

781×	`associate-/l*_binary64`
687×	`fma-def_binary64`
255×	`*-commutative_binary64`
234×	`+-commutative_binary64`
200×	`associate-+r+_binary64`

Counts

149 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	789	8170
1	2819	7767
2	5097	7767

prune378.0ms (2.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	211	7	218

Error

0.0b

Counts

218 → 7

Alt Table

Status	Error	Program
	35.8b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	26.9b	(-.f64 x (+.f64 (.f64 (/.f64 y t) z) (.f64 1/2 (-.f64 (.f64 (/.f64 y t) (.f64 z z)) (/.f64 (.f64 (.f64 y y) (*.f64 z z)) t)))))
▶	11.2b	(-.f64 x (/.f64 (expm1.f64 z) (/.f64 t y)))
	21.3b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
✓	1.4b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	1.5b	(-.f64 x (pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1))

Compiler

Compiled 13752 to 8169 computations (40.6% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(/.f64 (expm1.f64 z) (/.f64 t y))

series17.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

17.0ms

(/.f64 (expm1.f64 z) (/.f64 t y))

rewrite48.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

794×	`log1p-expm1-u_binary64`
794×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`
71×	`add-log-exp_binary64`
70×	`add-cube-cbrt_binary64`

Counts

1 → 45

Calls

1 calls:

46.0ms

(/.f64 (expm1.f64 z) (/.f64 t y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	148	9
2	2036	9
3	5012	9
0	0	0
1	0	0

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

706×	`distribute-rgt-out_binary64`
634×	`associate-/r/_binary64`
370×	`associate-/l/_binary64`
351×	`associate-r_binary64`
311×	`associate-l_binary64`

Counts

81 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	400
1	106	398
2	233	394
3	597	380
4	2090	364
5	4760	364
6	4958	364
7	4934	364

prune49.0ms (0.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	1	2	3
Picked	1	0	1
Done	1	2	3
Total	57	6	63

Error

Counts

63 → 6

Alt Table

Status	Error	Program
	35.8b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	11.5b	(-.f64 x (*.f64 (expm1.f64 z) (/.f64 y t)))
	21.3b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
✓	1.5b	(-.f64 x (pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1))
	10.4b	(-.f64 x (*.f64 y (/.f64 (expm1.f64 z) t)))

Compiler

Compiled 849 to 357 computations (58% saved)

regimes790.0ms (5.4%)

Accuracy

Total 0.1b remaining (36.4%)

Threshold costs 0.1b (36.4%)

Counts

67 → 3

Compiler

Compiled 15015 to 10093 computations (32.8% saved)

bsearch31.0ms (0.2%)

Steps

Iters	Range		Point
2	2.011777823653556e-41	3.80351646596604e-32	1.776953096329963e-34
1	-7.339284761581247e-122	-6.17299498054091e-123	-2.139802579946953e-122

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	29	52
2	44	52
3	56	52
4	65	52
5	69	52
6	70	52
7	70	52

end92.0ms (0.6%)

Compiler: Compiled 168 to 96 computations (42.9% saved)

Details

analyze1.6s (11.3%)

sample7.4s (50.9%)

simplify246.0ms (1.7%)

prune5.0ms (0%)

localize7.0ms (0%)

series833.0ms (5.7%)

rewrite49.0ms (0.3%)

simplify96.0ms (0.7%)

prune165.0ms (1.1%)

localize9.0ms (0.1%)

series582.0ms (4%)

rewrite47.0ms (0.3%)

simplify45.0ms (0.3%)

prune130.0ms (0.9%)

localize8.0ms (0.1%)

series1.6s (11.2%)

rewrite56.0ms (0.4%)

simplify121.0ms (0.8%)

prune378.0ms (2.6%)

localize6.0ms (0%)

series17.0ms (0.1%)

rewrite48.0ms (0.3%)

simplify72.0ms (0.5%)

prune49.0ms (0.3%)

regimes790.0ms (5.4%)

bsearch31.0ms (0.2%)

simplify5.0ms (0%)

end92.0ms (0.6%)

Profiling