Details

analyze569.0ms (6.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	74.9%	25.1%	3
0%	74.9%	25.1%	4
0%	62.4%	37.6%	5
0%	56.2%	43.8%	6
6.2%	49.9%	43.8%	7
9.4%	43.7%	47%	8
14%	37.4%	48.5%	9
21.1%	30.4%	48.5%	10
24.6%	26.1%	49.3%	11
28.7%	21.6%	49.7%	12
33.4%	16.9%	49.7%	13
35.8%	14.3%	49.9%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.3s (14.6%)

Results

1.1s	8255×	body	128	valid
6.0ms	62×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify144.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

3353×	`fma-neg_binary64`
476×	`distribute-rgt-in_binary64`
425×	`unsub-neg_binary64`
361×	`fma-def_binary64`
308×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	12
2	36	12
3	76	12
4	131	12
5	231	12
6	342	12
7	678	12
8	1365	12
9	2068	12
10	2356	12
11	2518	12
12	2627	12
13	2660	12
14	2664	12
15	2866	12
16	2767	12
17	2779	12
18	2791	12
19	2799	12
20	2799	12
21	5311	12

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series355.0ms (4%)

Counts

3 → 96

Calls

3 calls:

193.0ms	(*.f64 x (log.f64 y))
91.0ms	(-.f64 (*.f64 x (log.f64 y)) z)
71.0ms	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)

rewrite79.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

503×	`fma-def_binary64`
463×	`log-prod_binary64`
303×	`fma-neg_binary64`
275×	`egg-rr`
172×	`expm1-udef_binary64`

Counts

3 → 275

Calls

3 calls:

73.0ms	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)
73.0ms	(-.f64 (*.f64 x (log.f64 y)) z)
73.0ms	(*.f64 x (log.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	179	27
2	2442	27
3	5093	27
0	0	0
1	0	0

simplify192.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

3264×	`fma-neg_binary64`
798×	`associate--r-_binary64`
593×	`fma-def_binary64`
426×	`sub-neg_binary64`
392×	`unsub-neg_binary64`

Counts

371 → 291

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	813
1	93	813
2	205	813
3	372	813
4	894	813
5	1824	813
6	1860	813
7	1754	813
8	1856	813
9	1896	813
10	1906	813
11	1959	813
12	1920	813
13	1920	813
14	4536	813
15	5250	813

prune222.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	282	9	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	282	10	292

Error

0.0b

Counts

292 → 10

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)
	43.3b	(-.f64 (.f64 (-.f64 (pow.f64 (.f64 x (log.f64 y)) 3) (pow.f64 z 3)) (/.f64 1 (fma.f64 z (fma.f64 x (log.f64 y) z) (pow.f64 (*.f64 x (log.f64 y)) 2)))) y)
	31.2b	(-.f64 (.f64 (-.f64 (pow.f64 (.f64 x (log.f64 y)) 2) (*.f64 z z)) (/.f64 1 (fma.f64 x (log.f64 y) z))) y)
	31.1b	(-.f64 (-.f64 (pow.f64 (sqrt.f64 (*.f64 x (log.f64 y))) 2) z) y)
	0.4b	(-.f64 (-.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 y))) 3) z) y)
▶	0.4b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	30.4b	(-.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (*.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 z)) y)
	18.7b	(-.f64 (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
	42.8b	(-.f64 (/.f64 (-.f64 (pow.f64 (.f64 x (log.f64 y)) 3) (pow.f64 z 3)) (fma.f64 z (fma.f64 x (log.f64 y) z) (pow.f64 (.f64 x (log.f64 y)) 2))) y)

Compiler

Compiled 5032 to 1467 computations (70.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z))
✓	0.3b	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (log.f64 y)) 2)
✓	0.5b	(cbrt.f64 (log.f64 y))

series2.5s (28%)

Counts

4 → 84

Calls

4 calls:

1.1s	(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z))
889.0ms	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2))
275.0ms	(pow.f64 (cbrt.f64 (log.f64 y)) 2)
259.0ms	(cbrt.f64 (log.f64 y))

rewrite77.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

798×	`log1p-expm1-u_binary64`
798×	`expm1-log1p-u_binary64`
240×	`egg-rr`
172×	`prod-diff_binary64`
106×	`add-sqr-sqrt_binary64`

Counts

4 → 240

Calls

4 calls:

70.0ms	(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z))
70.0ms	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2))
70.0ms	(pow.f64 (cbrt.f64 (log.f64 y)) 2)
70.0ms	(cbrt.f64 (log.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	45
1	217	33
2	2130	33
3	5084	33
0	0	0
1	0	0

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

562×	`unsub-neg_binary64`
413×	`associate-r_binary64`
402×	`associate-l_binary64`
363×	`distribute-rgt-neg-in_binary64`
350×	`neg-sub0_binary64`

Counts

324 → 256

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	745
1	105	745
2	184	745
3	501	745
4	2021	745
5	4354	745
6	4949	745

prune250.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	278	4	282
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	283	9	292

Error

Counts

292 → 9

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)
	0.5b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) x)) 3) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	0.5b	(-.f64 (fma.f64 (*.f64 x (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2)))) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (-.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 y))) 3) z) y)
▶	0.3b	(-.f64 (fma.f64 (*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2))) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	0.3b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (pow.f64 (log.f64 y) 2) 1/3)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
✓	0.4b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	30.4b	(-.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (*.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 z)) y)

Compiler

Compiled 7072 to 2764 computations (60.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2)))
	0.5b	(cbrt.f64 (log.f64 y))
✓	0.5b	(cbrt.f64 (pow.f64 (log.f64 y) 2))
✓	0.5b	(pow.f64 (log.f64 y) 2)

series1.2s (13.5%)

Counts

3 → 44

Calls

3 calls:

813.0ms	(*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2)))
371.0ms	(cbrt.f64 (pow.f64 (log.f64 y) 2))
23.0ms	(pow.f64 (log.f64 y) 2)

rewrite200.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

581×	`log1p-expm1-u_binary64`
581×	`expm1-log1p-u_binary64`
319×	`log-prod_binary64`
178×	`pow2_binary64`
125×	`expm1-udef_binary64`

Counts

3 → 69

Calls

3 calls:

199.0ms	(*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2)))
199.0ms	(cbrt.f64 (pow.f64 (log.f64 y) 2))
199.0ms	(pow.f64 (log.f64 y) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	154	25
2	1561	25
3	5000	25
4	4919	25
0	0	0
1	0	0

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-neg_binary64`
590×	`associate-l_binary64`
548×	`unsub-neg_binary64`
547×	`unswap-sqr_binary64`
428×	`fma-def_binary64`

Counts

113 → 76

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	424
1	55	408
2	88	408
3	252	408
4	608	408
5	2304	408
6	4153	408
7	4922	408
8	4888	408

prune116.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	102	9	111

Error

Counts

111 → 9

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)
	0.5b	(-.f64 (fma.f64 (*.f64 x (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2)))) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (-.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 y))) 3) z) y)
✓	0.3b	(-.f64 (fma.f64 (*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2))) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
▶	0.3b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (pow.f64 (log.f64 y) 2) 1/3)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	1.2b	(-.f64 (fma.f64 (*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2))) (log1p.f64 (expm1.f64 (cbrt.f64 (log.f64 y)))) (neg.f64 z)) y)
✓	0.4b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	30.4b	(-.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (*.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 z)) y)

Compiler

Compiled 2194 to 1108 computations (49.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 x (pow.f64 (pow.f64 (log.f64 y) 2) 1/3))
	0.5b	(cbrt.f64 (log.f64 y))
	0.5b	(pow.f64 (log.f64 y) 2)
✓	1.2b	(pow.f64 (pow.f64 (log.f64 y) 2) 1/3)

series989.0ms (11.1%)

Counts

2 → 32

Calls

2 calls:

713.0ms	(*.f64 x (pow.f64 (pow.f64 (log.f64 y) 2) 1/3))
276.0ms	(pow.f64 (pow.f64 (log.f64 y) 2) 1/3)

rewrite45.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

670×	`log1p-expm1-u_binary64`
670×	`expm1-log1p-u_binary64`
348×	`log-prod_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`

Counts

2 → 42

Calls

2 calls:

44.0ms	(*.f64 x (pow.f64 (pow.f64 (log.f64 y) 2) 1/3))
44.0ms	(pow.f64 (pow.f64 (log.f64 y) 2) 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	183	19
2	1785	19
3	5140	19
0	0	0
1	0	0

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-neg_binary64`
590×	`associate-l_binary64`
548×	`unsub-neg_binary64`
547×	`unswap-sqr_binary64`
428×	`fma-def_binary64`

Counts

74 → 47

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	344
1	55	328
2	88	328
3	252	328
4	608	328
5	2304	328
6	4153	328
7	4922	328
8	4888	328

prune114.0ms (1.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	99	9	108

Error

Counts

108 → 9

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)
	0.5b	(-.f64 (fma.f64 (*.f64 x (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2)))) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (-.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 y))) 3) z) y)
✓	0.3b	(-.f64 (fma.f64 (*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2))) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
✓	0.3b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (pow.f64 (log.f64 y) 2) 1/3)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	1.2b	(-.f64 (fma.f64 (*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2))) (log1p.f64 (expm1.f64 (cbrt.f64 (log.f64 y)))) (neg.f64 z)) y)
✓	0.4b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	30.4b	(-.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (*.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 z)) y)

Compiler

Compiled 2121 to 1082 computations (49% saved)

regimes147.0ms (1.6%)

Accuracy

Total 0.1b remaining (69.7%)

Threshold costs 0.1b (69.7%)

Counts

36 → 1

Compiler

Compiled 2350 to 1524 computations (35.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	12
2	21	12
3	25	12
4	27	12
5	27	12

end123.0ms (1.4%)

Compiler: Compiled 175 to 114 computations (34.9% saved)

Details

analyze569.0ms (6.4%)

sample1.3s (14.6%)

simplify144.0ms (1.6%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series355.0ms (4%)

rewrite79.0ms (0.9%)

simplify192.0ms (2.1%)

prune222.0ms (2.5%)

localize13.0ms (0.1%)

series2.5s (28%)

rewrite77.0ms (0.9%)

simplify75.0ms (0.8%)

prune250.0ms (2.8%)

localize11.0ms (0.1%)

series1.2s (13.5%)

rewrite200.0ms (2.2%)

simplify84.0ms (0.9%)

prune116.0ms (1.3%)

localize14.0ms (0.2%)

series989.0ms (11.1%)

rewrite45.0ms (0.5%)

simplify91.0ms (1%)

prune114.0ms (1.3%)

regimes147.0ms (1.6%)

simplify2.0ms (0%)

end123.0ms (1.4%)

Profiling