Details

analyze530.0ms (5.5%)

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%	74.9%	25.1%	3
0%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
0%	31.2%	68.8%	7
0%	31.2%	68.8%	8
0%	31.2%	68.8%	9
0%	28.1%	71.9%	10
4.7%	21.8%	73.5%	11
4.7%	21.8%	73.5%	12
7%	19.5%	73.5%	13
8.2%	17.5%	74.3%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample2.3s (24.4%)

Results

1.1s	6355×	body	128	valid
453.0ms	492×	body	1024	valid
405.0ms	771×	body	512	valid
219.0ms	636×	body	256	valid
50.0ms	292×	body	128	invalid
2.0ms	2×	body	2048	valid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

735×	`unsub-neg_binary64`
674×	`sub-neg_binary64`
591×	`distribute-rgt-in_binary64`
584×	`fma-def_binary64`
542×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	31	23
2	65	23
3	129	23
4	308	23
5	765	23
6	1527	23
7	2231	23
8	2172	23
9	2249	23
10	2264	23
11	2274	23
12	3084	23
13	5202	23

prune4.0ms (0%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 (-.f64 x 1) (log.f64 y) (*.f64 (-.f64 z 1) (log1p.f64 (neg.f64 y)))) t)
	7.4b	(-.f64 (+.f64 (.f64 (-.f64 x 1) (log.f64 y)) (.f64 (-.f64 z 1) (log.f64 (-.f64 1 y)))) t)

Compiler

Compiled 116 to 85 computations (26.7% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 z 1) (log1p.f64 (neg.f64 y)))
✓	0.2b	(fma.f64 (-.f64 x 1) (log.f64 y) (*.f64 (-.f64 z 1) (log1p.f64 (neg.f64 y))))

series237.0ms (2.5%)

Counts

2 → 60

Calls

2 calls:

182.0ms	(fma.f64 (-.f64 x 1) (log.f64 y) (*.f64 (-.f64 z 1) (log1p.f64 (neg.f64 y))))
55.0ms	(*.f64 (-.f64 z 1) (log1p.f64 (neg.f64 y)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-l_binary64`
7×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 36

Calls

2 calls:

6.0ms	(*.f64 (-.f64 z 1) (log1p.f64 (neg.f64 y)))
0.0ms	(fma.f64 (-.f64 x 1) (log.f64 y) (*.f64 (-.f64 z 1) (log1p.f64 (neg.f64 y))))

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-neg_binary64`
472×	`sub-neg_binary64`
368×	`cancel-sign-sub-inv_binary64`
336×	`distribute-rgt-in_binary64`
311×	`distribute-neg-in_binary64`

Counts

96 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	2517
1	700	2204
2	2581	2155
3	4920	2151
4	5178	2151

prune104.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	3	122

Error

0.1b

Counts

122 → 3

Alt Table

Status	Error	Program
	39.2b	(-.f64 (log.f64 (*.f64 (pow.f64 (-.f64 1 y) (+.f64 z -1)) (pow.f64 y (+.f64 x -1)))) t)
▶	0.1b	(-.f64 (+.f64 (*.f64 (log.f64 y) x) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))) t)
	0.7b	(-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x 1) (log.f64 y) (.f64 (-.f64 z 1) (log1p.f64 (neg.f64 y))))) (cbrt.f64 (fma.f64 (-.f64 x 1) (log.f64 y) (.f64 (-.f64 z 1) (log1p.f64 (neg.f64 y)))))) (cbrt.f64 (fma.f64 (-.f64 x 1) (log.f64 y) (*.f64 (-.f64 z 1) (log1p.f64 (neg.f64 y)))))) t)

Compiler

Compiled 3370 to 1954 computations (42% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (log.f64 y) x) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y))))
✓	0.0b	(fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))
✓	0.3b	(*.f64 (log.f64 y) x)

series537.0ms (5.6%)

Counts

3 → 68

Calls

3 calls:

235.0ms	(+.f64 (*.f64 (log.f64 y) x) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y))))
210.0ms	(*.f64 (log.f64 y) x)
92.0ms	(fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 46

Calls

3 calls:

3.0ms	(+.f64 (*.f64 (log.f64 y) x) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y))))
3.0ms	(*.f64 (log.f64 y) x)
0.0ms	(fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))

simplify115.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-neg_binary64`
456×	`sub-neg_binary64`
416×	`distribute-rgt-in_binary64`
358×	`cancel-sign-sub-inv_binary64`
309×	`distribute-neg-in_binary64`

Counts

114 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	212	2829
1	688	2534
2	2452	2418
3	4525	2414
4	4998	2414
5	4962	2414

prune149.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	127	6	133
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	129	7	136

Error

0.0b

Counts

136 → 7

Alt Table

Status	Error	Program
	26.6b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 x (log.f64 y)) 3) (pow.f64 (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z) (neg.f64 (log.f64 y))) 3)) (fma.f64 (.f64 x (log.f64 y)) (.f64 x (log.f64 y)) (.f64 (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z) (neg.f64 (log.f64 y))) (+.f64 (.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z)) (.f64 (log.f64 y) (-.f64 -1 x)))))) t)
	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 y) x)) (cbrt.f64 (.f64 (log.f64 y) x))) (cbrt.f64 (*.f64 (log.f64 y) x))) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))) t)
	0.5b	(-.f64 (+.f64 (.f64 (.f64 (log.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))) t)
▶	0.1b	(-.f64 (+.f64 (.f64 -1 (.f64 x (log.f64 (/.f64 1 y)))) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))) t)
	0.5b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (*.f64 (cbrt.f64 (log.f64 y)) x)) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))) t)
	39.2b	(-.f64 (log.f64 (*.f64 (pow.f64 (-.f64 1 y) (+.f64 z -1)) (pow.f64 y (+.f64 x -1)))) t)
	32.1b	(-.f64 (+.f64 (.f64 (.f64 (log.f64 y) (sqrt.f64 x)) (sqrt.f64 x)) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))) t)

Compiler

Compiled 4105 to 2006 computations (51.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 -1 (.f64 x (log.f64 (/.f64 1 y)))) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y))))
✓	0.0b	(log.f64 (/.f64 1 y))
	0.0b	(fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))
✓	0.3b	(*.f64 x (log.f64 (/.f64 1 y)))

series511.0ms (5.3%)

Counts

3 → 64

Calls

3 calls:

254.0ms	(+.f64 (.f64 -1 (.f64 x (log.f64 (/.f64 1 y)))) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y))))
237.0ms	(*.f64 x (log.f64 (/.f64 1 y)))
19.0ms	(log.f64 (/.f64 1 y))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`log-prod_binary64`
65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
63×	`times-frac_binary64`
56×	`add-sqr-sqrt_binary64`

Counts

3 → 148

Calls

3 calls:

9.0ms	(+.f64 (.f64 -1 (.f64 x (log.f64 (/.f64 1 y)))) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y))))
5.0ms	(*.f64 x (log.f64 (/.f64 1 y)))
2.0ms	(log.f64 (/.f64 1 y))

simplify136.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-neg_binary64`
404×	`distribute-rgt-in_binary64`
282×	`sub-neg_binary64`
269×	`cancel-sign-sub-inv_binary64`
242×	`distribute-neg-in_binary64`

Counts

212 → 264

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	258	4582
1	666	3970
2	2398	3826
3	4670	3822
4	4987	3822

prune458.0ms (4.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	310	2	312
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	314	5	319

Error

Counts

319 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (.f64 (.f64 (log.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))) x) -1) (fma.f64 x (log.f64 (cbrt.f64 y)) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z) (neg.f64 (log.f64 y))))) t)
	26.6b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 x (log.f64 y)) 3) (pow.f64 (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z) (neg.f64 (log.f64 y))) 3)) (fma.f64 (.f64 x (log.f64 y)) (.f64 x (log.f64 y)) (.f64 (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z) (neg.f64 (log.f64 y))) (+.f64 (.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z)) (.f64 (log.f64 y) (-.f64 -1 x)))))) t)
	39.2b	(-.f64 (log.f64 (*.f64 (pow.f64 (-.f64 1 y) (+.f64 z -1)) (pow.f64 y (+.f64 x -1)))) t)
	0.2b	(-.f64 (+.f64 (.f64 -1 (.f64 (*.f64 x (sqrt.f64 (neg.f64 (log.f64 y)))) (sqrt.f64 (log.f64 (/.f64 1 y))))) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))) t)
✓	0.1b	(-.f64 (+.f64 (.f64 -1 (.f64 x (log.f64 (/.f64 1 y)))) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))) t)

Compiler

Compiled 9649 to 5443 computations (43.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (log.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y)))) x)
✓	0.3b	(/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.7b	(cbrt.f64 y)

series1.8s (19.2%)

Counts

4 → 60

Calls

4 calls:

1.7s	(.f64 (log.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y)))) x)
67.0ms	(/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
36.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
30.0ms	(cbrt.f64 y)

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-sqr-sqrt_binary64`
20×	`associate-l_binary64`
19×	`cbrt-prod_binary64`
19×	`add-exp-log_binary64`

Counts

4 → 124

Calls

4 calls:

6.0ms	(.f64 (log.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y)))) x)
6.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
5.0ms	(/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)

simplify104.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

929×	`fma-def_binary64`
506×	`log-prod_binary64`
361×	`fma-neg_binary64`
355×	`unsub-neg_binary64`
310×	`times-frac_binary64`

Counts

184 → 187

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	2021
1	252	1631
2	825	1476
3	2298	1357
4	4081	1345
5	4952	1345

prune319.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	225	5	230

Error

Counts

230 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (.f64 (.f64 (log.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))) x) -1) (fma.f64 x (log.f64 (cbrt.f64 y)) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z) (neg.f64 (log.f64 y))))) t)
	26.6b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 x (log.f64 y)) 3) (pow.f64 (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z) (neg.f64 (log.f64 y))) 3)) (fma.f64 (.f64 x (log.f64 y)) (.f64 x (log.f64 y)) (.f64 (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z) (neg.f64 (log.f64 y))) (+.f64 (.f64 (log1p.f64 (neg.f64 y)) (+.f64 -1 z)) (.f64 (log.f64 y) (-.f64 -1 x)))))) t)
	39.2b	(-.f64 (log.f64 (*.f64 (pow.f64 (-.f64 1 y) (+.f64 z -1)) (pow.f64 y (+.f64 x -1)))) t)
	0.2b	(-.f64 (+.f64 (.f64 -1 (.f64 (*.f64 x (sqrt.f64 (neg.f64 (log.f64 y)))) (sqrt.f64 (log.f64 (/.f64 1 y))))) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))) t)
✓	0.1b	(-.f64 (+.f64 (.f64 -1 (.f64 x (log.f64 (/.f64 1 y)))) (fma.f64 (log1p.f64 (neg.f64 y)) (+.f64 z -1) (neg.f64 (log.f64 y)))) t)

Compiler

Compiled 7712 to 3475 computations (54.9% saved)

regimes1.8s (18.2%)

Accuracy

Total 0.1b remaining (75.5%)

Threshold costs 0.1b (75.5%)

Counts

174 → 1

Compiler

Compiled 37455 to 26279 computations (29.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	28	31
2	35	31
3	39	31
4	40	31
5	39	31

end128.0ms (1.3%)

Compiler: Compiled 218 to 146 computations (33% saved)

Details

analyze530.0ms (5.5%)

sample2.3s (24.4%)

simplify91.0ms (0.9%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series237.0ms (2.5%)

rewrite8.0ms (0.1%)

simplify97.0ms (1%)

prune104.0ms (1.1%)

localize12.0ms (0.1%)

series537.0ms (5.6%)

rewrite8.0ms (0.1%)

simplify115.0ms (1.2%)

prune149.0ms (1.5%)

localize21.0ms (0.2%)

series511.0ms (5.3%)

rewrite33.0ms (0.3%)

simplify136.0ms (1.4%)

prune458.0ms (4.8%)

localize22.0ms (0.2%)

series1.8s (19.2%)

rewrite23.0ms (0.2%)

simplify104.0ms (1.1%)

prune319.0ms (3.3%)

regimes1.8s (18.2%)

simplify3.0ms (0%)

end128.0ms (1.3%)

Profiling