Details

analyze561.0ms (10.4%)

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%	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
35.9%	60.8%	3.3%	9
44.1%	48%	7.9%	10
54.8%	36.9%	8.3%	11
57.6%	31.5%	10.9%	12
61.9%	24%	14.1%	13
67.2%	18.6%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	28×	body	128	invalid

Compiler

Compiled 28 to 22 computations (21.4% saved)

simplify41.0ms (0.8%)

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

prune5.0ms (0.1%)

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

3.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.6b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.4b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series10.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

10.0ms

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

rewrite15.0ms (0.3%)

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:

11.0ms

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

simplify99.0ms (1.8%)

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

prune69.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	7	76

Error

0.0b

Counts

76 → 7

Alt Table

Status	Error	Program
	31.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	16.7b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (*.f64 z z))) (+.f64 (fma.f64 y z 1) z))
▶	2.3b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	3.6b	(+.f64 (.f64 (.f64 y z) x) (*.f64 (-.f64 1 z) x))
	34.0b	(+.f64 (.f64 (fma.f64 y z 1) x) (.f64 (*.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z)) x))
	3.9b	(+.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))
	16.7b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 1686 to 818 computations (51.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (.f64 z x)) x)
✓	0.0b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	4.6b	(.f64 y (.f64 z x))

series30.0ms (0.6%)

Counts

3 → 60

Calls

3 calls:

11.0ms	(.f64 y (.f64 z x))
10.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
9.0ms	(+.f64 (.f64 y (.f64 z x)) x)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 56

Calls

3 calls:

6.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
4.0ms	(+.f64 (.f64 y (.f64 z x)) x)
4.0ms	(.f64 y (.f64 z x))

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-neg_binary64`
502×	`fma-def_binary64`
318×	`cancel-sign-sub-inv_binary64`
279×	`distribute-rgt-in_binary64`
247×	`distribute-lft-in_binary64`

Counts

116 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1397
1	285	1233
2	896	1196
3	2752	1195
4	4487	1195
5	4963	1195

prune95.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	103	7	110

Error

0.0b

Counts

110 → 7

Alt Table

Status	Error	Program
▶	2.3b	(-.f64 (fma.f64 (.f64 x z) y x) (.f64 z x))
	31.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	33.5b	(.f64 (-.f64 (.f64 y x) x) z)
	16.7b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (*.f64 z z))) (+.f64 (fma.f64 y z 1) z))
	3.6b	(+.f64 (.f64 (.f64 y z) x) (*.f64 (-.f64 1 z) x))
	25.2b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (.f64 z x)))) x) (.f64 z x))
	2.5b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))) x) (*.f64 z x))

Compiler

Compiled 1980 to 557 computations (71.9% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (.f64 x z) y x) (.f64 z x))
✓	2.3b	(fma.f64 (*.f64 x z) y x)

series24.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

13.0ms	(fma.f64 (*.f64 x z) y x)
11.0ms	(-.f64 (fma.f64 (.f64 x z) y x) (.f64 z x))

rewrite6.0ms (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:

4.0ms	(-.f64 (fma.f64 (.f64 x z) y x) (.f64 z x))
0.0ms	(fma.f64 (*.f64 x z) y x)

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

670×	`associate-+l+_binary64`
281×	`distribute-rgt-out_binary64`
267×	`associate-l_binary64`
245×	`associate-r_binary64`
244×	`fma-def_binary64`

Counts

103 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	1288
1	165	1082
2	507	1057
3	2206	1056
4	5380	1056

prune44.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	63	7	70

Error

0.0b

Counts

70 → 7

Alt Table

Status	Error	Program
✓	2.3b	(-.f64 (fma.f64 (.f64 x z) y x) (.f64 z x))
	31.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	33.5b	(.f64 (-.f64 (.f64 y x) x) z)
	16.7b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (*.f64 z z))) (+.f64 (fma.f64 y z 1) z))
	3.6b	(+.f64 (.f64 (.f64 y z) x) (*.f64 (-.f64 1 z) x))
	25.2b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (.f64 z x)))) x) (.f64 z x))
▶	2.5b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))) x) (*.f64 z x))

Compiler

Compiled 1241 to 410 computations (67% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (*.f64 z x))))
	4.6b	(.f64 y (.f64 z x))
✓	13.1b	(cbrt.f64 (.f64 y (.f64 z x)))

series2.4s (43.8%)

Counts

3 → 108

Calls

3 calls:

1.6s

(*.f64 (cbrt.f64 (*.f64 y (*.f64 z x))) (cbrt.f64 (*.f64 y (*.f64 z x))))

700.0ms

(cbrt.f64 (*.f64 y (*.f64 z x)))

51.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 y (*.f64 z x))) (cbrt.f64 (*.f64 y (*.f64 z x)))) (cbrt.f64 (*.f64 y (*.f64 z x))))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 y (*.f64 z x))) (cbrt.f64 (*.f64 y (*.f64 z x)))) (cbrt.f64 (*.f64 y (*.f64 z x))))

5.0ms

(*.f64 (cbrt.f64 (*.f64 y (*.f64 z x))) (cbrt.f64 (*.f64 y (*.f64 z x))))

2.0ms

(cbrt.f64 (*.f64 y (*.f64 z x)))

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

640×	`unswap-sqr_binary64`
348×	`fma-neg_binary64`
314×	`exp-sum_binary64`
297×	`exp-prod_binary64`
260×	`unsub-neg_binary64`

Counts

187 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	3163
1	387	2879
2	865	2337
3	2290	2071
4	5245	2071

prune287.0ms (5.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	256	1	257
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	256	8	264

Error

Counts

264 → 8

Alt Table

Status	Error	Program
✓	2.3b	(-.f64 (fma.f64 (.f64 x z) y x) (.f64 z x))
	31.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	33.5b	(.f64 (-.f64 (.f64 y x) x) z)
	16.7b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (*.f64 z z))) (+.f64 (fma.f64 y z 1) z))
	2.5b	(-.f64 (+.f64 (.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (.f64 z x)) (cbrt.f64 (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))) x) (*.f64 z x))
	3.6b	(+.f64 (.f64 (.f64 y z) x) (*.f64 (-.f64 1 z) x))
	25.2b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (.f64 z x)))) x) (.f64 z x))
✓	2.5b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))) x) (*.f64 z x))

Compiler

Compiled 7914 to 1722 computations (78.2% saved)

regimes687.0ms (12.8%)

Accuracy

Total 0.2b remaining (95.1%)

Threshold costs 0.2b (95.1%)

Counts

60 → 3

Compiler

Compiled 7928 to 4730 computations (40.3% saved)

bsearch2.0ms (0%)

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

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

54×	`distribute-rgt-neg-in_binary64`
44×	`cancel-sign-sub-inv_binary64`
38×	`distribute-lft-neg-in_binary64`
34×	`distribute-neg-in_binary64`
33×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	67
1	52	67
2	85	67
3	118	65
4	149	65
5	167	65
6	173	65
7	187	65
8	219	65
9	236	65
10	246	65
11	251	65
12	265	65
13	274	65
14	281	65
15	283	65
16	279	65

end1.0ms (0%)

Compiler: Compiled 47 to 30 computations (36.2% saved)

sample693.0ms (12.9%)

Algorithm

1×

intervals

Results

294.0ms	8000×	body	128	valid
27.0ms	736×	body	128	invalid

Compiler

Compiled 222 to 122 computations (45% saved)

Iter	Nodes	Cost
0	26	67
1	52	67
2	85	67
3	118	65
4	149	65
5	167	65
6	173	65
7	187	65
8	219	65
9	236	65
10	246	65
11	251	65
12	265	65
13	274	65
14	281	65
15	283	65
16	279	65

Iter	Nodes	Cost
0	26	67
1	52	67
2	85	67
3	118	65
4	149	65
5	167	65
6	173	65
7	187	65
8	219	65
9	236	65
10	246	65
11	251	65
12	265	65
13	274	65
14	281	65
15	283	65
16	279	65

Details

analyze561.0ms (10.4%)

sample22.0ms (0.4%)

simplify41.0ms (0.8%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series10.0ms (0.2%)

rewrite15.0ms (0.3%)

simplify99.0ms (1.8%)

prune69.0ms (1.3%)

localize6.0ms (0.1%)

series30.0ms (0.6%)

rewrite16.0ms (0.3%)

simplify88.0ms (1.6%)

prune95.0ms (1.8%)

localize12.0ms (0.2%)

series24.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify66.0ms (1.2%)

prune44.0ms (0.8%)

localize9.0ms (0.2%)

series2.4s (43.8%)

rewrite21.0ms (0.4%)

simplify96.0ms (1.8%)

prune287.0ms (5.3%)

regimes687.0ms (12.8%)

bsearch2.0ms (0%)

simplify13.0ms (0.3%)

end1.0ms (0%)

sample693.0ms (12.9%)

Profiling

Iter	Nodes	Cost
0	26	67
1	52	67
2	85	67
3	118	65
4	149	65
5	167	65
6	173	65
7	187	65
8	219	65
9	236	65
10	246	65
11	251	65
12	265	65
13	274	65
14	281	65
15	283	65
16	279	65