Details

analyze441.0ms (4.8%)

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 18 to 13 computations (27.8% saved)

sample2.5s (27.3%)

Results

1.0s	6007×	body	128	valid
566.0ms	710×	body	1024	valid
410.0ms	879×	body	512	valid
220.0ms	639×	body	256	valid
43.0ms	287×	body	128	invalid
20.0ms	21×	body	2048	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-neg_binary64`
326×	`fma-def_binary64`
173×	`distribute-rgt-in_binary64`
134×	`unsub-neg_binary64`
124×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	25	17
2	46	17
3	71	17
4	112	17
5	173	17
6	293	17
7	437	17
8	681	17
9	1080	17
10	1312	17
11	1523	17
12	1539	17
13	1539	17
14	1492	17

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 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
	9.4b	(-.f64 (+.f64 (.f64 x (log.f64 y)) (.f64 z (log.f64 (-.f64 1 y)))) t)

Compiler

Compiled 92 to 61 computations (33.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series622.0ms (6.8%)

Counts

3 → 108

Calls

3 calls:

236.0ms	(*.f64 z (log1p.f64 (neg.f64 y)))
223.0ms	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
162.0ms	(fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y))))

rewrite131.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

714×	`prod-diff_binary64`
470×	`fma-udef_binary64`
320×	`fma-def_binary64`
207×	`fma-neg_binary64`
195×	`expm1-udef_binary64`

Counts

3 → 147

Calls

3 calls:

127.0ms	(*.f64 z (log1p.f64 (neg.f64 y)))
127.0ms	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
127.0ms	(fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	226	33
2	2572	33
3	4693	33
4	4716	33
5	4954	33
0	0	0
1	0	0

simplify127.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
580×	`associate--r+_binary64`
405×	`unsub-neg_binary64`
368×	`distribute-neg-in_binary64`
243×	`sub-neg_binary64`

Counts

255 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1970
1	471	1834
2	1472	1770
3	4706	1770
4	4990	1770
5	4999	1770
6	4970	1770

prune180.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	218	8	226
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	219	9	228

Error

0.1b

Counts

228 → 9

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) t)
	9.4b	(-.f64 (+.f64 (.f64 x (log.f64 y)) (.f64 z (log.f64 (-.f64 1 y)))) t)
	37.7b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
	25.7b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (log.f64 y)) (-.f64 (*.f64 z (log1p.f64 y)) t))
	33.8b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y))) 3)) t)
	37.3b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y)))) 2) t)
	11.4b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y)))) 3) t)
	1.0b	(-.f64 (*.f64 (log.f64 y) x) (fma.f64 y z t))
	11.4b	(fma.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))

Compiler

Compiled 4665 to 1680 computations (64% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series541.0ms (5.9%)

Counts

3 → 92

Calls

3 calls:

204.0ms	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) t)
199.0ms	(*.f64 (log.f64 y) x)
138.0ms	(fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x))

rewrite133.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

714×	`prod-diff_binary64`
470×	`fma-udef_binary64`
320×	`fma-def_binary64`
207×	`fma-neg_binary64`
195×	`expm1-udef_binary64`

Counts

3 → 147

Calls

3 calls:

128.0ms	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) t)
128.0ms	(fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x))
128.0ms	(*.f64 (log.f64 y) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	226	33
2	2572	33
3	4693	33
4	4716	33
5	4958	33
0	0	0
1	0	0

simplify106.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-+l+_binary64`
510×	`associate--r+_binary64`
491×	`fma-def_binary64`
458×	`unsub-neg_binary64`
305×	`associate-+r+_binary64`

Counts

239 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	1681
1	379	1585
2	1193	1454
3	4513	1454
4	4893	1454
5	4954	1454
6	5080	1454

prune133.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	207	8	215

Error

0.0b

Counts

215 → 8

Alt Table

Status	Error	Program
	37.7b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
▶	0.6b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 3)) t)
	11.4b	(fma.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
	32.7b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (pow.f64 (sqrt.f64 (*.f64 (log.f64 y) x)) 2)) t)
	9.4b	(-.f64 (+.f64 (.f64 x (log.f64 y)) (.f64 z (log.f64 (-.f64 1 y)))) t)
	17.7b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (expm1.f64 (log1p.f64 (*.f64 (log.f64 y) x)))) t)
	23.6b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (cbrt.f64 (*.f64 (pow.f64 (log.f64 y) 3) (pow.f64 x 3)))) t)
	1.0b	(-.f64 (*.f64 (log.f64 y) x) (fma.f64 y z t))

Compiler

Compiled 4163 to 1402 computations (66.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (log1p.f64 (neg.f64 y)) z (pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 3))
	0.2b	(*.f64 (log.f64 y) x)
✓	0.6b	(cbrt.f64 (*.f64 (log.f64 y) x))
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 3)

series1.9s (20.9%)

Counts

3 → 84

Calls

3 calls:

694.0ms	(fma.f64 (log1p.f64 (neg.f64 y)) z (pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 3))
619.0ms	(pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 3)
604.0ms	(cbrt.f64 (*.f64 (log.f64 y) x))

rewrite63.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

852×	`expm1-log1p-u_binary64`
851×	`log1p-expm1-u_binary64`
376×	`prod-diff_binary64`
108×	`add-sqr-sqrt_binary64`
100×	`add-cbrt-cube_binary64`

Counts

3 → 84

Calls

3 calls:

61.0ms	(fma.f64 (log1p.f64 (neg.f64 y)) z (pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 3))
61.0ms	(cbrt.f64 (*.f64 (log.f64 y) x))
61.0ms	(pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	224	26
2	2264	26
3	5847	26
0	0	0
1	0	0

simplify127.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-neg_binary64`
445×	`sub-neg_binary64`
352×	`fma-def_binary64`
224×	`distribute-neg-in_binary64`
221×	`unsub-neg_binary64`

Counts

168 → 124

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	107	1139
1	314	1095
2	877	1043
3	2802	1019
4	4684	1015
5	4936	1015
6	4989	1015
7	4923	1015

prune149.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	141	9	150

Error

0.0b

Counts

150 → 9

Alt Table

Status	Error	Program
	11.4b	(fma.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
	32.7b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (pow.f64 (sqrt.f64 (*.f64 (log.f64 y) x)) 2)) t)
	31.6b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)))) t)
	9.4b	(-.f64 (+.f64 (.f64 x (log.f64 y)) (.f64 z (log.f64 (-.f64 1 y)))) t)
	0.5b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (.f64 (cbrt.f64 (log.f64 y)) x))) t)
▶	0.5b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 2)))) t)
	0.7b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (pow.f64 (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 x)) 3)) t)
	23.6b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (cbrt.f64 (*.f64 (pow.f64 (log.f64 y) 3) (pow.f64 x 3)))) t)
	1.0b	(-.f64 (*.f64 (log.f64 y) x) (fma.f64 y z t))

Compiler

Compiled 2969 to 1345 computations (54.7% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (log.f64 y))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 2)
✓	0.6b	(cbrt.f64 x)
	0.6b	(cbrt.f64 (*.f64 (log.f64 y) x))

series942.0ms (10.3%)

Counts

3 → 48

Calls

3 calls:

643.0ms	(pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 2)
266.0ms	(cbrt.f64 (log.f64 y))
33.0ms	(cbrt.f64 x)

rewrite52.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

701×	`log1p-expm1-u_binary64`
701×	`expm1-log1p-u_binary64`
149×	`expm1-udef_binary64`
149×	`log1p-udef_binary64`
146×	`log-pow_binary64`

Counts

3 → 66

Calls

3 calls:

51.0ms	(cbrt.f64 (log.f64 y))
51.0ms	(pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 2)
51.0ms	(cbrt.f64 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	187	19
2	1899	19
3	4911	19
0	0	0
1	0	0

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-neg_binary64`
336×	`unswap-sqr_binary64`
293×	`unsub-neg_binary64`
257×	`distribute-rgt-in_binary64`
249×	`exp-sum_binary64`

Counts

114 → 77

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	53	520
1	142	520
2	257	508
3	848	492
4	2500	428
5	3936	420
6	4773	420
7	4958	420
8	4884	420

prune117.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	106	11	117

Error

0.0b

Counts

117 → 11

Alt Table

Status	Error	Program
	0.7b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (.f64 (.f64 (cbrt.f64 (cbrt.f64 (log.f64 y))) (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 y))) 2)) (.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (.f64 (log.f64 y) x)) 2)))) t)
	23.6b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (cbrt.f64 (*.f64 (pow.f64 (log.f64 y) 3) (pow.f64 x 3)))) t)
	1.0b	(-.f64 (*.f64 (log.f64 y) x) (fma.f64 y z t))
	8.3b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (log.f64 y)))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 y))) 4)))))) t)
	11.4b	(fma.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
	0.6b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x (log.f64 y)))))))) t)
	31.6b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)))) t)
	9.4b	(-.f64 (+.f64 (.f64 x (log.f64 y)) (.f64 z (log.f64 (-.f64 1 y)))) t)
	0.5b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (.f64 (cbrt.f64 (log.f64 y)) x))) t)
✓	0.5b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 2)))) t)
	0.7b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (pow.f64 (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 x)) 3)) t)

Compiler

Compiled 2992 to 1198 computations (60% saved)

regimes483.0ms (5.3%)

Accuracy

Total 0.1b remaining (66.7%)

Threshold costs 0.1b (66.7%)

Counts

72 → 1

Compiler

Compiled 8096 to 5481 computations (32.3% 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	11	17
1	18	17
2	23	17
3	26	17
4	27	17
5	27	17

end183.0ms (2%)

Compiler: Compiled 284 to 185 computations (34.9% saved)

Details

analyze441.0ms (4.8%)

sample2.5s (27.3%)

simplify56.0ms (0.6%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series622.0ms (6.8%)

rewrite131.0ms (1.4%)

simplify127.0ms (1.4%)

prune180.0ms (2%)

localize9.0ms (0.1%)

series541.0ms (5.9%)

rewrite133.0ms (1.4%)

simplify106.0ms (1.2%)

prune133.0ms (1.5%)

localize13.0ms (0.1%)

series1.9s (20.9%)

rewrite63.0ms (0.7%)

simplify127.0ms (1.4%)

prune149.0ms (1.6%)

localize21.0ms (0.2%)

series942.0ms (10.3%)

rewrite52.0ms (0.6%)

simplify102.0ms (1.1%)

prune117.0ms (1.3%)

regimes483.0ms (5.3%)

simplify3.0ms (0%)

end183.0ms (2%)

Profiling