Details

analyze1.1s (8.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	90.4%	9.6%	9
0%	45.2%	54.8%	10
0%	45.2%	54.8%	11
0%	45.2%	54.8%	12
0%	45.2%	54.8%	13
0%	44.4%	55.6%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample5.5s (40.2%)

Results

3.2s	16458×	body	128	invalid
1.6s	7566×	body	128	valid
162.0ms	295×	body	512	valid
127.0ms	141×	body	1024	valid
92.0ms	254×	body	256	valid
83.0ms	126×	body	512	invalid
57.0ms	142×	body	256	invalid
46.0ms	55×	body	1024	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
557×	`associate-/l*_binary64`
456×	`unswap-sqr_binary64`
365×	`*-commutative_binary64`
332×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	34	25
2	73	25
3	158	25
4	405	25
5	1252	25
6	2771	25
7	4527	25
8	5117	25

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

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 84 to 54 computations (35.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log.f64 z) t)
✓	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.2b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.3b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series1.3s (9.2%)

Counts

4 → 147

Calls

4 calls:

556.0ms	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
352.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))
304.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
55.0ms	(-.f64 (log.f64 z) t)

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 119

Calls

4 calls:

7.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
4.0ms	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
4.0ms	(-.f64 (log.f64 z) t)
0.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

simplify187.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

685×	`associate-l_binary64`
571×	`fma-def_binary64`
463×	`fma-neg_binary64`
195×	`*-commutative_binary64`
138×	`sub-neg_binary64`

Counts

266 → 269

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	585	8192
1	1704	7336
2	4889	7336
3	5236	7336

prune253.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	265	4	269
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	266	4	270

Error

0.0b

Counts

270 → 4

Alt Table

Status	Error	Program
	2.0b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
	14.2b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
▶	0.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
	35.9b	(exp.f64 (+.f64 (log.f64 x) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 10123 to 3642 computations (64% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 x) (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
	0.3b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(cbrt.f64 x)

series1.1s (8%)

Counts

3 → 96

Calls

3 calls:

1.0s	(.f64 (cbrt.f64 x) (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
37.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
31.0ms	(cbrt.f64 x)

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
12×	`associate-l_binary64`

Counts

3 → 80

Calls

3 calls:

5.0ms	(.f64 (cbrt.f64 x) (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify146.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

799×	`associate-l_binary64`
533×	`fma-neg_binary64`
402×	`*-commutative_binary64`
387×	`fma-def_binary64`
123×	`cancel-sign-sub-inv_binary64`

Counts

176 → 167

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	396	6519
1	1290	5783
2	4788	5783
3	5244	5783

prune212.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	256	4	260

Error

0.0b

Counts

260 → 4

Alt Table

Status	Error	Program
▶	2.0b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
	14.2b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
✓	0.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
	35.9b	(exp.f64 (+.f64 (log.f64 x) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 11055 to 3432 computations (69% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
✓	0.3b	(-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (.f64 y t)))
✓	0.3b	(*.f64 (log.f64 z) y)
✓	0.5b	(fma.f64 a b (*.f64 y t))

series712.0ms (5.2%)

Counts

4 → 156

Calls

4 calls:

284.0ms	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
226.0ms	(*.f64 (log.f64 z) y)
192.0ms	(-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (.f64 y t)))
9.0ms	(fma.f64 a b (*.f64 y t))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

4 → 80

Calls

4 calls:

7.0ms	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
3.0ms	(-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (.f64 y t)))
3.0ms	(*.f64 (log.f64 z) y)
0.0ms	(fma.f64 a b (*.f64 y t))

simplify162.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-neg_binary64`
598×	`cancel-sign-sub-inv_binary64`
425×	`associate-r_binary64`
350×	`associate-l_binary64`
263×	`distribute-rgt-neg-in_binary64`

Counts

236 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	4310
1	704	3999
2	2715	3888
3	4583	3888
4	4988	3888
5	4961	3888

prune138.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	179	4	183

Error

0.0b

Counts

183 → 4

Alt Table

Status	Error	Program
▶	1.7b	(/.f64 x (exp.f64 (fma.f64 a b (*.f64 y (-.f64 t (log.f64 z))))))
	35.9b	(exp.f64 (+.f64 (log.f64 x) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (.f64 y t)))))
✓	2.0b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
✓	0.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))

Compiler

Compiled 4635 to 1072 computations (76.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (log.f64 z))
✓	0.2b	(*.f64 y (-.f64 t (log.f64 z)))
✓	0.3b	(/.f64 x (exp.f64 (fma.f64 a b (*.f64 y (-.f64 t (log.f64 z))))))
✓	0.5b	(fma.f64 a b (*.f64 y (-.f64 t (log.f64 z))))

series911.0ms (6.6%)

Counts

4 → 135

Calls

4 calls:

416.0ms	(/.f64 x (exp.f64 (fma.f64 a b (*.f64 y (-.f64 t (log.f64 z))))))
256.0ms	(*.f64 y (-.f64 t (log.f64 z)))
183.0ms	(fma.f64 a b (*.f64 y (-.f64 t (log.f64 z))))
55.0ms	(-.f64 t (log.f64 z))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
41×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
20×	`pow1_binary64`

Counts

4 → 140

Calls

4 calls:

7.0ms	(*.f64 y (-.f64 t (log.f64 z)))
4.0ms	(-.f64 t (log.f64 z))
3.0ms	(/.f64 x (exp.f64 (fma.f64 a b (*.f64 y (-.f64 t (log.f64 z))))))
0.0ms	(fma.f64 a b (*.f64 y (-.f64 t (log.f64 z))))

simplify124.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

838×	`times-frac_binary64`
720×	`fma-def_binary64`
233×	`associate-r_binary64`
232×	`associate-l_binary64`
209×	`fma-neg_binary64`

Counts

275 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	329	5607
1	714	4811
2	2528	4796
3	5002	4796

prune189.0ms (1.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	226	4	230

Error

0.0b

Counts

230 → 4

Alt Table

Status	Error	Program
	35.9b	(exp.f64 (-.f64 (log.f64 x) (fma.f64 y (-.f64 t (log.f64 z)) (*.f64 a b))))
✓	1.7b	(/.f64 x (exp.f64 (fma.f64 a b (*.f64 y (-.f64 t (log.f64 z))))))
✓	2.0b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
✓	0.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))

Compiler

Compiled 5600 to 1436 computations (74.4% saved)

regimes1.4s (10.3%)

Accuracy

Total 0.2b remaining (87.9%)

Threshold costs 0.2b (87.9%)

Counts

165 → 1

Compiler

Compiled 32141 to 22002 computations (31.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	32	34
2	40	34
3	45	34
4	47	34
5	47	34

end80.0ms (0.6%)

Compiler: Compiled 142 to 94 computations (33.8% saved)

Details

analyze1.1s (8.1%)

sample5.5s (40.2%)

simplify51.0ms (0.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series1.3s (9.2%)

rewrite22.0ms (0.2%)

simplify187.0ms (1.4%)

prune253.0ms (1.8%)

localize17.0ms (0.1%)

series1.1s (8%)

rewrite15.0ms (0.1%)

simplify146.0ms (1.1%)

prune212.0ms (1.5%)

localize12.0ms (0.1%)

series712.0ms (5.2%)

rewrite22.0ms (0.2%)

simplify162.0ms (1.2%)

prune138.0ms (1%)

localize11.0ms (0.1%)

series911.0ms (6.6%)

rewrite24.0ms (0.2%)

simplify124.0ms (0.9%)

prune189.0ms (1.4%)

regimes1.4s (10.3%)

simplify4.0ms (0%)

end80.0ms (0.6%)

Profiling