Details

analyze1.9s (10.7%)

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
13.1%	74.3%	12.7%	12
16.1%	70.5%	13.5%	13
18.6%	68%	13.5%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample223.0ms (1.2%)

Algorithm

1×

intervals

Results

29.0ms	52×	body	1024	valid
15.0ms	13×	body	2048	valid
12.0ms	134×	body	128	valid
8.0ms	31×	body	512	valid
5.0ms	26×	body	256	valid
3.0ms	50×	body	128	nan
2.0ms	7×	body	512	nan
2.0ms	23×	body	128	overflowed
1.0ms	5×	body	1024	nan
0.0ms	2×	body	256	nan

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify249.0ms (1.4%)

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

prune4.0ms (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

0.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.9b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.3b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.8b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.6s (9.1%)

Counts

3 → 108

Calls

3 calls:

825.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
493.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
327.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
53×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

3 → 111

Calls

3 calls:

6.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
2.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
0.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))

simplify153.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

350×	`fma-def_binary64`
308×	`fma-neg_binary64`
277×	`associate-+r+_binary64`
238×	`associate-+l+_binary64`
202×	`associate-r_binary64`

Counts

219 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	500	8918
1	1470	5721
2	4900	5719
3	5158	5719

prune194.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	223	5	228
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	224	5	229

Error

0.2b

Counts

229 → 5

Alt Table

Status	Error	Program
	1.2b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	21.0b	(-.f64 x (*.f64 (/.f64 y t) z))
	1.0b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	18.3b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
▶	0.9b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

Compiler

Compiled 8006 to 2874 computations (64.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	0.3b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.8b	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))

series1.4s (8%)

Counts

2 → 84

Calls

2 calls:

857.0ms	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))
580.0ms	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

7.0ms	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))
3.0ms	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

simplify117.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
324×	`sub-neg_binary64`
278×	`fma-neg_binary64`
249×	`cancel-sign-sub-inv_binary64`
186×	`+-commutative_binary64`

Counts

142 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	3778
1	913	3303
2	3086	3202
3	4958	3202
4	5009	3202

prune219.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	200	5	205

Error

0.2b

Counts

205 → 5

Alt Table

Status	Error	Program
	1.2b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	21.0b	(-.f64 x (*.f64 (/.f64 y t) z))
▶	1.0b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	18.3b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
✓	0.9b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

Compiler

Compiled 5792 to 2913 computations (49.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
	0.3b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.3b	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))
✓	4.8b	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)

series1.7s (9.7%)

Counts

3 → 84

Calls

3 calls:

831.0ms	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)
616.0ms	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
292.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

2.0ms	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)
0.0ms	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
0.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))

simplify95.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-def_binary64`
313×	`associate-r_binary64`
272×	`associate-+l+_binary64`
271×	`associate-l_binary64`
177×	`associate-/r*_binary64`

Counts

136 → 175

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	464	4678
1	1404	4129
2	5039	4129

prune216.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	218	7	225

Error

0.2b

Counts

225 → 7

Alt Table

Status	Error	Program
	21.0b	(-.f64 x (*.f64 (/.f64 y t) z))
	1.3b	(-.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) (cbrt.f64 t))))
▶	1.2b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
✓	1.0b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	18.3b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
✓	0.9b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	21.8b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (*.f64 y z))) t))

Compiler

Compiled 7759 to 4150 computations (46.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))
✓	0.4b	(.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))
	4.8b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
✓	14.8b	(cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

series4.5s (24.9%)

Counts

3 → 108

Calls

3 calls:

2.1s

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

1.6s

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

769.0ms

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

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`cbrt-prod_binary64`
78×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

3 → 160

Calls

3 calls:

11.0ms

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

10.0ms

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

2.0ms

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

simplify272.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

756×	`associate-/l*_binary64`
419×	`*-commutative_binary64`
242×	`+-commutative_binary64`
192×	`fma-def_binary64`
182×	`associate-+r+_binary64`

Counts

268 → 363

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1164	18311
1	3562	16895
2	5831	16895

prune1.1s (6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	722	1	723
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	723	7	730

Error

0.2b

Counts

730 → 7

Alt Table

Status	Error	Program
✓	1.2b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	1.3b	(-.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) (cbrt.f64 t))))
	11.5b	(-.f64 x (*.f64 (/.f64 y t) (expm1.f64 z)))
✓	1.0b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	18.3b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
✓	0.9b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	21.8b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (*.f64 y z))) t))

Compiler

Compiled 50354 to 20353 computations (59.6% saved)

regimes767.0ms (4.3%)

Accuracy

Total 0.8b remaining (79.7%)

Threshold costs 0.8b (79.7%)

Counts

92 → 1

Compiler

Compiled 17154 to 11160 computations (34.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	20	14
2	24	14
3	27	14
4	28	14
5	28	14

end0.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample3.1s (17.1%)

Algorithm

1×

intervals

Results

1.0s	1776×	body	1024	valid
413.0ms	1322×	body	512	valid
366.0ms	3859×	body	128	valid
294.0ms	295×	body	2048	valid
134.0ms	748×	body	256	valid
98.0ms	1550×	body	128	nan
75.0ms	217×	body	1024	nan
60.0ms	837×	body	128	overflowed
55.0ms	249×	body	512	nan
24.0ms	156×	body	256	nan
1.0ms	18×	body	128	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 167 to 104 computations (37.7% saved)

Details

analyze1.9s (10.7%)

sample223.0ms (1.2%)

simplify249.0ms (1.4%)

prune4.0ms (0%)

localize8.0ms (0%)

series1.6s (9.1%)

rewrite20.0ms (0.1%)

simplify153.0ms (0.8%)

prune194.0ms (1.1%)

localize9.0ms (0.1%)

series1.4s (8%)

rewrite13.0ms (0.1%)

simplify117.0ms (0.7%)

prune219.0ms (1.2%)

localize11.0ms (0.1%)

series1.7s (9.7%)

rewrite5.0ms (0%)

simplify95.0ms (0.5%)

prune216.0ms (1.2%)

localize11.0ms (0.1%)

series4.5s (24.9%)

rewrite44.0ms (0.2%)

simplify272.0ms (1.5%)

prune1.1s (6%)

regimes767.0ms (4.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (17.1%)

Profiling