Details

analyze1.8s (9.6%)

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)

sample6.7s (36.7%)

Results

2.1s	1541×	body	8192	exit
1.5s	1835×	body	1024	valid
900.0ms	1434×	body	512	valid
720.0ms	3860×	body	128	valid
391.0ms	314×	body	2048	valid
339.0ms	1697×	body	128	invalid
338.0ms	813×	body	256	valid
114.0ms	196×	body	1024	invalid
97.0ms	242×	body	512	invalid
47.0ms	168×	body	256	invalid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify248.0ms (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

2.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.2b	(-.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 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.0b	(*.f64 y (expm1.f64 z))
✓	0.5b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	5.9b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.6s (8.8%)

Counts

4 → 132

Calls

4 calls:

806.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
493.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
297.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
8.0ms	(*.f64 y (expm1.f64 z))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

7.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
3.0ms	(*.f64 y (expm1.f64 z))
2.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
0.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))

simplify174.0ms (1%)

Algorithm

1×	egg-herbie

Rules

360×	`fma-def_binary64`
345×	`fma-neg_binary64`
243×	`associate-r_binary64`
238×	`associate-+l+_binary64`
236×	`associate-l_binary64`

Counts

263 → 257

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	527	9322
1	1512	6066
2	4776	6064
3	5068	6064

prune186.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	252	5	257
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	252	6	258

Error

0.3b

Counts

258 → 6

Alt Table

Status	Error	Program
▶	2.5b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	17.8b	(-.f64 x (*.f64 (/.f64 y t) z))
	20.3b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	39.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) 3)) (fma.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) (+.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) x) (.f64 x x)))
	18.4b	x
✓	2.2b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 8461 to 3071 computations (63.7% saved)

localize9.0ms (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	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))
	0.5b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	5.9b	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)

series1.7s (9.2%)

Counts

3 → 84

Calls

3 calls:

768.0ms	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)
627.0ms	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
290.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))

rewrite7.0ms (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)))))

simplify88.0ms (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

prune212.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	220	6	226

Error

0.2b

Counts

226 → 6

Alt Table

Status	Error	Program
	17.8b	(-.f64 x (*.f64 (/.f64 y t) z))
▶	13.1b	(-.f64 x (-.f64 (/.f64 (exp.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t) (/.f64 1 t)))
	20.3b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	39.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) 3)) (fma.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) (+.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) x) (.f64 x x)))
	18.4b	x
✓	2.2b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 7722 to 4132 computations (46.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (exp.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)
✓	0.2b	(exp.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))
	0.5b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	1.8b	(-.f64 (/.f64 (exp.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t) (/.f64 1 t))

series4.0s (21.6%)

Counts

3 → 96

Calls

3 calls:

1.7s

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

1.6s

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

649.0ms

(exp.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))

rewrite62.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

275×	`times-frac_binary64`
227×	`add-sqr-sqrt_binary64`
224×	`*-un-lft-identity_binary64`
210×	`add-cube-cbrt_binary64`
169×	`prod-diff_binary64`

Counts

3 → 267

Calls

3 calls:

14.0ms

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

3.0ms

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

2.0ms

(exp.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))

simplify338.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

451×	`fma-neg_binary64`
327×	`fma-def_binary64`
288×	`+-commutative_binary64`
213×	`associate-/r*_binary64`
199×	`associate-+r+_binary64`

Counts

363 → 411

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	473	18520
1	1244	13287
2	4716	13281
3	5120	13281

prune421.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	456	0	456
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	456	6	462

Error

0.2b

Counts

462 → 6

Alt Table

Status	Error	Program
▶	17.8b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	13.1b	(-.f64 x (-.f64 (/.f64 (exp.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t) (/.f64 1 t)))
	20.3b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	39.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) 3)) (fma.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) (+.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) x) (.f64 x x)))
	18.4b	x
✓	2.2b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 19430 to 9068 computations (53.3% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	4.0b	(*.f64 (/.f64 y t) z)

series26.0ms (0.1%)

Counts

2 → 84

Calls

2 calls:

14.0ms	(-.f64 x (*.f64 (/.f64 y t) z))
12.0ms	(*.f64 (/.f64 y t) z)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`

Counts

2 → 54

Calls

2 calls:

4.0ms	(*.f64 (/.f64 y t) z)
2.0ms	(-.f64 x (*.f64 (/.f64 y t) z))

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

695×	`times-frac_binary64`
638×	`fma-def_binary64`
348×	`associate-l_binary64`
278×	`distribute-rgt-neg-in_binary64`
273×	`associate-r_binary64`

Counts

138 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1358
1	244	1310
2	650	1283
3	2364	1283
4	4486	1283
5	4926	1283

prune56.0ms (0.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	91	8	99

Error

0.2b

Counts

99 → 8

Alt Table

Status	Error	Program
✓	17.8b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	13.1b	(-.f64 x (-.f64 (/.f64 (exp.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t) (/.f64 1 t)))
	20.3b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	17.9b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 y t)) (cbrt.f64 (/.f64 y t))) (*.f64 (cbrt.f64 (/.f64 y t)) z)))
	55.3b	(neg.f64 (/.f64 (*.f64 y z) t))
	39.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) 3)) (fma.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) (+.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) x) (.f64 x x)))
	18.4b	x
✓	2.2b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 1404 to 406 computations (71.1% saved)

regimes524.0ms (2.9%)

Accuracy

Total 0.9b remaining (85.1%)

Threshold costs 0.9b (85.1%)

Counts

70 → 1

Compiler

Compiled 11893 to 7883 computations (33.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
2	20	14
3	24	14
4	27	14
5	28	14
6	28	14

end97.0ms (0.5%)

Compiler: Compiled 165 to 97 computations (41.2% saved)

Details

analyze1.8s (9.6%)

sample6.7s (36.7%)

simplify248.0ms (1.4%)

prune4.0ms (0%)

localize8.0ms (0%)

series1.6s (8.8%)

rewrite22.0ms (0.1%)

simplify174.0ms (1%)

prune186.0ms (1%)

localize9.0ms (0.1%)

series1.7s (9.2%)

rewrite7.0ms (0%)

simplify88.0ms (0.5%)

prune212.0ms (1.2%)

localize12.0ms (0.1%)

series4.0s (21.6%)

rewrite62.0ms (0.3%)

simplify338.0ms (1.8%)

prune421.0ms (2.3%)

localize6.0ms (0%)

series26.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify78.0ms (0.4%)

prune56.0ms (0.3%)

regimes524.0ms (2.9%)

simplify3.0ms (0%)

end97.0ms (0.5%)

Profiling