Details

analyze423.0ms (5.6%)

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%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
34.3%	62.4%	3.3%	9
42.1%	49.9%	7.9%	10
53.8%	37.8%	8.3%	11
56.2%	33%	10.9%	12
60.3%	25.6%	14.1%	13
66.4%	19.4%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.1s (14.3%)

Results

821.0ms	8256×	body	128	valid
75.0ms	689×	body	128	invalid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify39.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
210×	`distribute-rgt-in_binary64`
164×	`distribute-lft-in_binary64`
139×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	47	11
3	132	11
4	334	11
5	640	11
6	965	11
7	1254	11
8	1262	11
9	1262	11
10	1191	11

prune3.0ms (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

2.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series10.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

10.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
17×	`add-cube-cbrt_binary64`
14×	`distribute-lft-in_binary64`

Counts

1 → 52

Calls

1 calls:

5.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

412×	`unsub-neg_binary64`
396×	`exp-prod_binary64`
359×	`distribute-rgt-in_binary64`
334×	`distribute-lft-in_binary64`
331×	`fma-def_binary64`

Counts

88 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1249
1	225	1167
2	784	1113
3	2358	1057
4	3941	1057
5	4982	1057
6	4909	1057

prune64.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Error

0.0b

Counts

76 → 7

Alt Table

Status	Error	Program
	2.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	2.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	13.8b	(+.f64 (.f64 (fma.f64 (sqrt.f64 (fma.f64 y z 1)) (sqrt.f64 (fma.f64 y z 1)) (neg.f64 (.f64 z 1))) x) (.f64 (fma.f64 (neg.f64 z) 1 (.f64 z 1)) x))
	3.2b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
▶	2.3b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 (.f64 z 1))) x) (.f64 (fma.f64 (neg.f64 z) 1 (*.f64 z 1)) x))
	3.3b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
	16.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 1733 to 855 computations (50.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 (.f64 z 1)))
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1)))
✓	2.0b	(.f64 (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 (*.f64 z 1))) x)
✓	2.1b	(cbrt.f64 (fma.f64 y z 1))

series2.6s (34.9%)

Counts

4 → 108

Calls

4 calls:

1.8s	(.f64 (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 (*.f64 z 1))) x)
825.0ms	(fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 (.f64 z 1)))
22.0ms	(*.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1)))
17.0ms	(cbrt.f64 (fma.f64 y z 1))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`pow1_binary64`

Counts

4 → 85

Calls

4 calls:

9.0ms	(.f64 (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 (*.f64 z 1))) x)
4.0ms	(*.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1)))
1.0ms	(cbrt.f64 (fma.f64 y z 1))
0.0ms	(fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 (.f64 z 1)))

simplify152.0ms (2%)

Algorithm

1×	egg-herbie

Rules

323×	`distribute-rgt-in_binary64`
306×	`fma-neg_binary64`
302×	`distribute-lft-in_binary64`
247×	`cancel-sign-sub-inv_binary64`
234×	`associate-/r*_binary64`

Counts

193 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	296	6352
1	841	5483
2	2459	4921
3	4603	4704
4	4956	4704

prune423.0ms (5.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	332	0	332
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	332	7	339

Error

0.0b

Counts

339 → 7

Alt Table

Status	Error	Program
▶	2.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	2.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	13.8b	(+.f64 (.f64 (fma.f64 (sqrt.f64 (fma.f64 y z 1)) (sqrt.f64 (fma.f64 y z 1)) (neg.f64 (.f64 z 1))) x) (.f64 (fma.f64 (neg.f64 z) 1 (.f64 z 1)) x))
	3.2b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	2.3b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 (.f64 z 1))) x) (.f64 (fma.f64 (neg.f64 z) 1 (*.f64 z 1)) x))
	3.3b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
	16.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 16252 to 10585 computations (34.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	0.3b	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	0.3b	(.f64 x (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z))))
✓	2.2b	(cbrt.f64 (-.f64 (fma.f64 y z 1) z))

series714.0ms (9.5%)

Counts

4 → 120

Calls

4 calls:

600.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z))))
77.0ms	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
27.0ms	(cbrt.f64 (-.f64 (fma.f64 y z 1) z))
10.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))

rewrite54.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
44×	`associate-*r/_binary64`
40×	`flip--_binary64`
40×	`flip3--_binary64`
38×	`cbrt-prod_binary64`

Counts

4 → 158

Calls

4 calls:

17.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
8.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z))))
8.0ms	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
2.0ms	(cbrt.f64 (-.f64 (fma.f64 y z 1) z))

simplify294.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

975×	`fma-def_binary64`
704×	`times-frac_binary64`
347×	`*-commutative_binary64`
234×	`+-commutative_binary64`
149×	`associate-+r+_binary64`

Counts

278 → 394

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	950	16210
1	3205	15465
2	4983	15465
3	4978	15465

prune841.0ms (11.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	542	2	544
Fresh	2	2	4
Picked	0	1	1
Done	1	1	2
Total	545	6	551

Error

0.0b

Counts

551 → 6

Alt Table

Status	Error	Program
✓	2.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	2.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	13.8b	(+.f64 (.f64 (fma.f64 (sqrt.f64 (fma.f64 y z 1)) (sqrt.f64 (fma.f64 y z 1)) (neg.f64 (.f64 z 1))) x) (.f64 (fma.f64 (neg.f64 z) 1 (.f64 z 1)) x))
▶	3.2b	(-.f64 (fma.f64 y (.f64 z x) x) (.f64 z x))
	17.1b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 z y 1) (fma.f64 z y 1)) (*.f64 z z))) (+.f64 z (fma.f64 z y 1)))
	16.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 33764 to 22513 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 y (.f64 z x) x) (.f64 z x))
✓	3.3b	(fma.f64 y (*.f64 z x) x)

series17.0ms (0.2%)

Counts

2 → 72

Calls

2 calls:

9.0ms	(-.f64 (fma.f64 y (.f64 z x) x) (.f64 z x))
7.0ms	(fma.f64 y (*.f64 z x) x)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-neg_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(-.f64 (fma.f64 y (.f64 z x) x) (.f64 z x))
0.0ms	(fma.f64 y (*.f64 z x) x)

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

670×	`associate-+l+_binary64`
279×	`distribute-rgt-out_binary64`
266×	`associate-l_binary64`
244×	`fma-def_binary64`
243×	`associate-r_binary64`

Counts

103 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	1261
1	163	1082
2	504	1057
3	2206	1056
4	5380	1056

prune44.0ms (0.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	70	6	76

Error

Counts

76 → 6

Alt Table

Status	Error	Program
✓	2.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	2.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	13.8b	(+.f64 (.f64 (fma.f64 (sqrt.f64 (fma.f64 y z 1)) (sqrt.f64 (fma.f64 y z 1)) (neg.f64 (.f64 z 1))) x) (.f64 (fma.f64 (neg.f64 z) 1 (.f64 z 1)) x))
	35.5b	(.f64 (-.f64 (.f64 y x) x) z)
✓	3.2b	(-.f64 (fma.f64 y (.f64 z x) x) (.f64 z x))
	17.1b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 z y 1) (fma.f64 z y 1)) (*.f64 z z))) (+.f64 z (fma.f64 z y 1)))

Compiler

Compiled 1209 to 330 computations (72.7% saved)

regimes389.0ms (5.2%)

Accuracy

Total 1.8b remaining (99.3%)

Threshold costs 0b (0%)

Counts

49 → 2

Compiler

Compiled 8087 to 5150 computations (36.3% saved)

bsearch2.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

64×	`distribute-rgt-neg-in_binary64`
58×	`cancel-sign-sub-inv_binary64`
40×	`distribute-lft-neg-in_binary64`
36×	`distribute-lft-neg-out_binary64`
35×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	41	45
2	64	45
3	82	45
4	98	45
5	106	45
6	116	45
7	134	45
8	148	45
9	170	45
10	199	45
11	242	45
12	278	45
13	303	45
14	314	45
15	316	45
16	312	45

end107.0ms (1.4%)

Compiler: Compiled 185 to 113 computations (38.9% saved)

Iter	Nodes	Cost
0	20	45
1	41	45
2	64	45
3	82	45
4	98	45
5	106	45
6	116	45
7	134	45
8	148	45
9	170	45
10	199	45
11	242	45
12	278	45
13	303	45
14	314	45
15	316	45
16	312	45

Iter	Nodes	Cost
0	20	45
1	41	45
2	64	45
3	82	45
4	98	45
5	106	45
6	116	45
7	134	45
8	148	45
9	170	45
10	199	45
11	242	45
12	278	45
13	303	45
14	314	45
15	316	45
16	312	45

Details

analyze423.0ms (5.6%)

sample1.1s (14.3%)

simplify39.0ms (0.5%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series10.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify90.0ms (1.2%)

prune64.0ms (0.8%)

localize15.0ms (0.2%)

series2.6s (34.9%)

rewrite19.0ms (0.2%)

simplify152.0ms (2%)

prune423.0ms (5.6%)

localize8.0ms (0.1%)

series714.0ms (9.5%)

rewrite54.0ms (0.7%)

simplify294.0ms (3.9%)

prune841.0ms (11.1%)

localize9.0ms (0.1%)

series17.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify59.0ms (0.8%)

prune44.0ms (0.6%)

regimes389.0ms (5.2%)

bsearch2.0ms (0%)

simplify43.0ms (0.6%)

end107.0ms (1.4%)

Profiling

Iter	Nodes	Cost
0	20	45
1	41	45
2	64	45
3	82	45
4	98	45
5	106	45
6	116	45
7	134	45
8	148	45
9	170	45
10	199	45
11	242	45
12	278	45
13	303	45
14	314	45
15	316	45
16	312	45