Details

analyze1.3s (21.1%)

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
0%	99.8%	0.2%	9
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (19.5%)

Results

995.0ms	8256×	body	128	valid
88.0ms	761×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify114.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1539×	`fma-neg_binary64`
1346×	`fma-def_binary64`
1046×	`div-sub_binary64`
750×	`associate-/r/_binary64`
420×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	49	16
3	96	16
4	183	16
5	339	16
6	657	16
7	1726	16
8	2830	16
9	2687	16
10	2951	16
11	3172	16
12	3258	16
13	4297	16
14	5213	16

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

11.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	11.1b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series57.0ms (0.9%)

Counts

2 → 69

Calls

2 calls:

51.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
6.0ms	(-.f64 x (*.f64 y z))

rewrite103.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

412×	`fma-def_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
195×	`fma-neg_binary64`
136×	`egg-rr`

Counts

2 → 136

Calls

2 calls:

100.0ms	(-.f64 x (*.f64 y z))
100.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	253	23
2	3617	23
3	4990	23
4	5001	23

simplify112.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

611×	`associate-/r*_binary64`
549×	`fma-def_binary64`
458×	`cancel-sign-sub-inv_binary64`
314×	`fma-neg_binary64`
212×	`associate-*l/_binary64`

Counts

205 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	2839
1	406	2698
2	1596	2491
3	4685	2491
4	5000	2491
5	4981	2491

prune140.0ms (2.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	167	9	176
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	167	10	177

Error

1.5b

Counts

177 → 10

Alt Table

Status	Error	Program
	11.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	44.2b	(/.f64 x t)
	33.9b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	36.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) 2)
	12.3b	(pow.f64 (cbrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) 3)
	39.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) 1) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
✓	11.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
▶	11.5b	(/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 a z)))
	41.2b	(/.f64 y a)
	12.3b	(.f64 (pow.f64 (cbrt.f64 (-.f64 x (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (/.f64 1 (-.f64 t (*.f64 z a)))))

Compiler

Compiled 4654 to 1457 computations (68.7% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	11.1b	(/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 a z)))

series53.0ms (0.9%)

Counts

1 → 60

Calls

1 calls:

52.0ms

(/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 a z)))

rewrite112.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

670×	`prod-diff_binary64`
505×	`fma-udef_binary64`
366×	`fma-def_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`

Counts

1 → 36

Calls

1 calls:

111.0ms

(/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 a z)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	240	14
2	2871	12
3	4839	12
4	4762	12
5	4951	12

simplify98.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

611×	`associate-/r*_binary64`
548×	`fma-def_binary64`
458×	`cancel-sign-sub-inv_binary64`
314×	`fma-neg_binary64`
213×	`associate-*l/_binary64`

Counts

96 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	2805
1	403	2664
2	1593	2457
3	4681	2457
4	4996	2457
5	4982	2457

prune53.0ms (0.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	74	10	84

Error

1.5b

Counts

84 → 10

Alt Table

Status	Error	Program
▶	11.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	44.2b	(/.f64 x t)
	33.9b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	36.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) 2)
	12.3b	(pow.f64 (cbrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) 3)
	39.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) 1) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
✓	11.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
✓	11.5b	(/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 a z)))
	41.2b	(/.f64 y a)
	12.3b	(.f64 (pow.f64 (cbrt.f64 (-.f64 x (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (/.f64 1 (-.f64 t (*.f64 z a)))))

Compiler

Compiled 2348 to 996 computations (57.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.2b	(/.f64 1 (-.f64 t (*.f64 z a)))
✓	11.1b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

series71.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

55.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
16.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))

rewrite70.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

409×	`fma-def_binary64`
258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
176×	`fma-neg_binary64`
147×	`add-sqr-sqrt_binary64`

Counts

2 → 69

Calls

2 calls:

69.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))
69.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	286	26
2	3693	26
3	5019	26

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

697×	`associate-/r*_binary64`
667×	`fma-def_binary64`
460×	`cancel-sign-sub-inv_binary64`
196×	`associate-/l/_binary64`
182×	`sub-neg_binary64`

Counts

165 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	3894
1	474	3733
2	1848	3465
3	4999	3465

prune150.0ms (2.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	208	10	218

Error

1.5b

Counts

218 → 10

Alt Table

Status	Error	Program
✓	11.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	44.2b	(/.f64 x t)
	33.9b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	36.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) 2)
	33.1b	(/.f64 (.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 y z) 2)) (/.f64 1 (-.f64 t (.f64 z a)))) (fma.f64 y z x))
	39.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) 1) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
✓	11.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
✓	11.5b	(/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 a z)))
	41.2b	(/.f64 y a)
▶	12.3b	(.f64 (pow.f64 (cbrt.f64 (-.f64 x (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (/.f64 1 (-.f64 t (*.f64 z a)))))

Compiler

Compiled 5394 to 1968 computations (63.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) 2)
✓	3.3b	(.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (/.f64 1 (-.f64 t (*.f64 z a))))
✓	4.7b	(.f64 (pow.f64 (cbrt.f64 (-.f64 x (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (/.f64 1 (-.f64 t (*.f64 z a)))))
✓	8.1b	(cbrt.f64 (-.f64 x (*.f64 y z)))

series266.0ms (4.4%)

Counts

4 → 192

Calls

4 calls:

98.0ms	(.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (/.f64 1 (-.f64 t (*.f64 z a))))
69.0ms	(pow.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) 2)
57.0ms	(.f64 (pow.f64 (cbrt.f64 (-.f64 x (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (/.f64 1 (-.f64 t (*.f64 z a)))))
41.0ms	(cbrt.f64 (-.f64 x (*.f64 y z)))

rewrite79.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

312×	`expm1-udef_binary64`
312×	`log1p-udef_binary64`
181×	`add-sqr-sqrt_binary64`
173×	`log1p-expm1-u_binary64`
173×	`expm1-log1p-u_binary64`

Counts

4 → 97

Calls

4 calls:

77.0ms	(pow.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) 2)
77.0ms	(.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (/.f64 1 (-.f64 t (*.f64 z a))))
77.0ms	(.f64 (pow.f64 (cbrt.f64 (-.f64 x (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (/.f64 1 (-.f64 t (*.f64 z a)))))
77.0ms	(cbrt.f64 (-.f64 x (*.f64 y z)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	58
1	367	55
2	4421	55
3	5260	55

simplify227.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

802×	`times-frac_binary64`
467×	`fma-def_binary64`
242×	`*-commutative_binary64`
210×	`sub-neg_binary64`
160×	`fma-neg_binary64`

Counts

289 → 326

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	663	11476
1	2414	11136
2	4973	11136
3	5009	11136

prune324.0ms (5.4%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	407	1	408
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	407	11	418

Error

1.5b

Counts

418 → 11

Alt Table

Status	Error	Program
	44.2b	(/.f64 x t)
	56.2b	(.f64 (pow.f64 (cbrt.f64 (-.f64 x (.f64 y z))) 2) (*.f64 (/.f64 1 t) (pow.f64 x 1/3)))
✓	11.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	33.9b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	36.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) 2)
	33.1b	(/.f64 (.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 y z) 2)) (/.f64 1 (-.f64 t (.f64 z a)))) (fma.f64 y z x))
	39.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) 1) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
✓	11.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
✓	11.5b	(/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 a z)))
	41.2b	(/.f64 y a)
✓	12.3b	(.f64 (pow.f64 (cbrt.f64 (-.f64 x (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (/.f64 1 (-.f64 t (*.f64 z a)))))

Compiler

Compiled 19835 to 9639 computations (51.4% saved)

regimes1.3s (21.3%)

Accuracy

Total 4.2b remaining (70.1%)

Threshold costs 0b (0%)

Counts

105 → 5

Compiler

Compiled 14576 to 8974 computations (38.4% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
12×	`sub-neg_binary64`
11×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	161
1	59	161
2	84	161
3	99	161
4	107	161
5	108	161
6	108	161

end134.0ms (2.2%)

Compiler: Compiled 445 to 209 computations (53% saved)

Details

analyze1.3s (21.1%)

sample1.2s (19.5%)

simplify114.0ms (1.9%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series57.0ms (0.9%)

rewrite103.0ms (1.7%)

simplify112.0ms (1.9%)

prune140.0ms (2.3%)

localize7.0ms (0.1%)

series53.0ms (0.9%)

rewrite112.0ms (1.9%)

simplify98.0ms (1.6%)

prune53.0ms (0.9%)

localize8.0ms (0.1%)

series71.0ms (1.2%)

rewrite70.0ms (1.2%)

simplify79.0ms (1.3%)

prune150.0ms (2.5%)

localize17.0ms (0.3%)

series266.0ms (4.4%)

rewrite79.0ms (1.3%)

simplify227.0ms (3.8%)

prune324.0ms (5.4%)

regimes1.3s (21.3%)

bsearch4.0ms (0.1%)

simplify6.0ms (0.1%)

end134.0ms (2.2%)

Profiling