Details

analyze919.0ms (21.2%)

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)

sample257.0ms (5.9%)

Algorithm

1×

intervals

Symmetry

(sort d2 d4)

Results

12.0ms	256×	body	128	valid
4.0ms	79×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify96.0ms (2.2%)

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)))

series17.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

17.0ms

(*.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:

9.0ms

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

simplify77.0ms (1.8%)

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 → 55

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

prune36.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	54	3	57

Error

Counts

57 → 3

Alt Table

Status	Error	Program
▶	31.9b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
	39.3b	(cbrt.f64 (.f64 (.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))) (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

Compiler

Compiled 929 to 209 computations (77.5% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 d1 (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
✓	0.2b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

series201.0ms (4.6%)

Counts

2 → 64

Calls

2 calls:

187.0ms	(*.f64 d1 (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
14.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
18×	`associate-r_binary64`
14×	`sqrt-div_binary64`
13×	`sqrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`

Counts

2 → 63

Calls

2 calls:

17.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
12.0ms	(*.f64 d1 (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

simplify104.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

792×	`fma-def_binary64`
678×	`distribute-rgt-in_binary64`
416×	`fma-neg_binary64`
327×	`cancel-sign-sub-inv_binary64`
274×	`associate-l_binary64`

Counts

127 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	216	3106
1	588	2775
2	1939	2644
3	4726	2634
4	4978	2634

prune51.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	131	3	134

Error

Counts

134 → 3

Alt Table

Status	Error	Program
✓	31.9b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
▶	39.3b	(cbrt.f64 (.f64 (.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))) (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

Compiler

Compiled 4160 to 910 computations (78.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.1b	(.f64 (.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))) (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
✓	0.3b	(.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))) (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
✓	37.5b	(cbrt.f64 (.f64 (.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))) (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))

series298.0ms (6.9%)

Counts

3 → 144

Calls

3 calls:

185.0ms

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

82.0ms

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

31.0ms

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

rewrite127.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

197×	`pow1_binary64`
138×	`associate-*r/_binary64`
86×	`pow-prod-down_binary64`
65×	`add-cbrt-cube_binary64`
60×	`flip-+_binary64`

Counts

3 → 194

Calls

3 calls:

29.0ms

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

29.0ms

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

19.0ms

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

simplify347.0ms (8%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
669×	`associate-l_binary64`
237×	`distribute-rgt-in_binary64`
228×	`distribute-lft-in_binary64`
180×	`+-commutative_binary64`

Counts

338 → 307

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	524	20510
1	1583	16816
2	4788	16816
3	5003	16816

prune309.0ms (7.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	472	0	472
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	472	3	475

Error

Counts

475 → 3

Alt Table

Status	Error	Program
✓	31.9b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
✓	39.3b	(cbrt.f64 (.f64 (.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))) (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

Compiler

Compiled 23504 to 6490 computations (72.4% saved)

regimes416.0ms (9.6%)

Accuracy

Total 0.0b remaining (17.4%)

Threshold costs 0.0b (17.4%)

Counts

79 → 1

Compiler

Compiled 8188 to 4709 computations (42.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	17	16
2	25	16
3	29	16
4	31	16
5	31	16

end9.0ms (0.2%)

Remove: (sort d2 d4)
Compiler: Compiled 45 to 27 computations (40% saved)

sample1000.0ms (23%)

Algorithm

1×

intervals

Results

415.0ms	8000×	body	128	valid
134.0ms	2432×	body	128	invalid

Compiler

Compiled 109 to 54 computations (50.5% saved)

Details

analyze919.0ms (21.2%)

sample257.0ms (5.9%)

simplify96.0ms (2.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series17.0ms (0.4%)

rewrite10.0ms (0.2%)

simplify77.0ms (1.8%)

prune36.0ms (0.8%)

localize8.0ms (0.2%)

series201.0ms (4.6%)

rewrite35.0ms (0.8%)

simplify104.0ms (2.4%)

prune51.0ms (1.2%)

localize12.0ms (0.3%)

series298.0ms (6.9%)

rewrite127.0ms (2.9%)

simplify347.0ms (8%)

prune309.0ms (7.1%)

regimes416.0ms (9.6%)

simplify2.0ms (0.1%)

end9.0ms (0.2%)

sample1000.0ms (23%)

Profiling