Details

analyze1.4s (22.1%)

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
6.2%	93.6%	0.2%	9
28.1%	68.6%	3.3%	10
29.6%	65.5%	4.9%	11
32%	61.7%	6.3%	12
35.5%	56.9%	7.6%	13
48%	38.7%	13.4%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
3.0ms	65×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify104.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1400×	`fma-neg_binary64`
654×	`fma-def_binary64`
233×	`sub-neg_binary64`
210×	`unsub-neg_binary64`
158×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	32	14
2	94	13
3	263	13
4	655	13
5	1556	13
6	1691	13
7	1500	13
8	1500	13
9	2739	13
10	2707	13
11	2707	13
12	2632	13

prune3.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 92 to 53 computations (42.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
6×	`associate-r_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`distribute-lft-out--_binary64`
3×	`distribute-lft-out_binary64`

Counts

1 → 27

Calls

1 calls:

8.0ms

(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

series33.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

33.0ms

(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

617×	`distribute-rgt-in_binary64`
603×	`distribute-lft-in_binary64`
446×	`fma-neg_binary64`
407×	`associate-l_binary64`
313×	`associate-r_binary64`

Counts

75 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	1262
1	195	1056
2	718	940
3	3249	940
4	4599	940
5	4980	940

prune32.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	142	3	145

Error

0.0b

Counts

145 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
▶	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
	1.5b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

Compiler

Compiled 893 to 211 computations (76.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	0.0b	(-.f64 (.f64 d1 d2) (.f64 d1 d3))
✓	0.0b	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`diff-log_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 64

Calls

3 calls:

6.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
5.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
2.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

series136.0ms (2.2%)

Counts

3 → 132

Calls

3 calls:

59.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
52.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
24.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

simplify111.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-l_binary64`
685×	`fma-def_binary64`
488×	`fma-neg_binary64`
459×	`distribute-rgt-in_binary64`
440×	`distribute-lft-in_binary64`

Counts

196 → 352

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2558
1	361	2139
2	1230	2096
3	4966	2096
4	5229	2096

prune81.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	351	1	352
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	351	4	355

Error

Counts

355 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
▶	1.2b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1))) (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)))) (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1))) (neg.f64 (*.f64 d1 d1)))
	1.5b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

Compiler

Compiled 2754 to 533 computations (80.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1))) (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))))
	1.3b	(cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1)))
	1.3b	(cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1)))
✓	1.3b	(cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1)))

rewrite75.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`cbrt-div_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 65

Calls

2 calls:

65.0ms

(*.f64 (cbrt.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1))) (cbrt.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1))))

4.0ms

(cbrt.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1)))

series1.1s (17.4%)

Counts

2 → 96

Calls

2 calls:

604.0ms

(*.f64 (cbrt.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1))) (cbrt.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1))))

457.0ms

(cbrt.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1)))

simplify225.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-def_binary64`
827×	`times-frac_binary64`
419×	`*-commutative_binary64`
210×	`+-commutative_binary64`
141×	`associate-+r+_binary64`

Counts

161 → 304

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1022	12973
1	3352	12320
2	5412	12320

prune513.0ms (8.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	640	0	640
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	640	4	644

Error

Counts

644 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	1.2b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1))) (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)))) (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1))) (neg.f64 (*.f64 d1 d1)))
▶	1.5b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

Compiler

Compiled 40436 to 15754 computations (61% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
	0.6b	(cbrt.f64 d1)
	0.6b	(cbrt.f64 d1)
✓	0.6b	(cbrt.f64 d1)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
1.0ms	(cbrt.f64 d1)

series556.0ms (9.1%)

Counts

2 → 24

Calls

2 calls:

332.0ms	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
223.0ms	(cbrt.f64 d1)

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune38.0ms (0.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	274	4	278

Error

Counts

278 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	1.2b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1))) (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)))) (cbrt.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1))) (neg.f64 (*.f64 d1 d1)))
✓	1.5b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

Compiler

Compiled 2259 to 475 computations (79% saved)

regimes460.0ms (7.5%)

Accuracy

Total 0.0b remaining (62.7%)

Threshold costs 0.0b (62.7%)

Compiler

Compiled 8333 to 4294 computations (48.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	18	17
2	28	17
3	34	17
4	37	17
5	37	17

end6.0ms (0.1%)

Remove: (sort d2 d4)
Compiler: Compiled 48 to 27 computations (43.8% saved)

sample1.0s (17.1%)

Algorithm

1×

intervals

Results

429.0ms	8000×	body	128	valid
136.0ms	2389×	body	128	invalid

Compiler

Compiled 138 to 69 computations (50% saved)

Details

analyze1.4s (22.1%)

sample42.0ms (0.7%)

simplify104.0ms (1.7%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

rewrite10.0ms (0.2%)

series33.0ms (0.5%)

simplify89.0ms (1.4%)

prune32.0ms (0.5%)

localize10.0ms (0.2%)

rewrite17.0ms (0.3%)

series136.0ms (2.2%)

simplify111.0ms (1.8%)

prune81.0ms (1.3%)

localize14.0ms (0.2%)

rewrite75.0ms (1.2%)

series1.1s (17.4%)

simplify225.0ms (3.7%)

prune513.0ms (8.4%)

localize10.0ms (0.2%)

rewrite7.0ms (0.1%)

series556.0ms (9.1%)

simplify75.0ms (1.2%)

prune38.0ms (0.6%)

regimes460.0ms (7.5%)

simplify3.0ms (0.1%)

end6.0ms (0.1%)

sample1.0s (17.1%)

Profiling