Details

analyze423.0ms (9.4%)

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
37.4%	62.4%	0.1%	8
40.6%	56.9%	2.5%	9
45.2%	50.7%	4%	10
57.7%	33.5%	8.7%	11
59.7%	29.4%	11%	12
62%	25%	13%	13
68.3%	17.4%	14.4%	14

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample969.0ms (21.6%)

Symmetry

(sort d2 d3)

Results

840.0ms	8215×	body	128	valid
72.0ms	707×	body	128	invalid
7.0ms	17×	body	512	valid
4.0ms	13×	body	1024	valid
2.0ms	11×	body	256	valid

Compiler

Compiled 50 to 35 computations (30% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

114×	`fma-def_binary64`
61×	`associate-+l+_binary64`
40×	`associate-+r+_binary64`
34×	`distribute-lft-out_binary64`
33×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	21	14
2	50	10
3	125	10
4	216	10
5	237	10
6	249	10
7	235	10

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 d2 (+.f64 d3 37)))
	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))

Compiler

Compiled 75 to 51 computations (32% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))

series9.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
5×	`associate-r_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`distribute-lft-out_binary64`
3×	`associate-l_binary64`

Counts

1 → 26

Calls

1 calls:

6.0ms

(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))

simplify61.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

961×	`distribute-rgt-in_binary64`
953×	`distribute-lft-in_binary64`
416×	`associate-l_binary64`
318×	`associate-r_binary64`
261×	`fma-def_binary64`

Counts

62 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	687
1	163	645
2	700	643
3	4006	643
4	4316	643
5	5142	643

prune34.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	48	4	52

Error

Counts

52 → 4

Alt Table

Status	Error	Program
	21.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
▶	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

Compiler

Compiled 768 to 461 computations (40% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 d3 5) d1)
✓	0.0b	(+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1))
✓	0.0b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))

series22.0ms (0.5%)

Counts

3 → 96

Calls

3 calls:

10.0ms	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
8.0ms	(+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1))
4.0ms	(*.f64 (+.f64 d3 5) d1)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 55

Calls

3 calls:

5.0ms	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
4.0ms	(*.f64 (+.f64 d3 5) d1)
4.0ms	(+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1))

simplify87.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-def_binary64`
695×	`fma-neg_binary64`
486×	`cancel-sign-sub-inv_binary64`
332×	`*-commutative_binary64`
298×	`associate-+l+_binary64`

Counts

151 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	1635
1	348	1544
2	1326	1485
3	3601	1483
4	4941	1483
5	4843	1483

prune67.0ms (1.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	108	4	112

Error

Counts

112 → 4

Alt Table

Status	Error	Program
	21.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

Compiler

Compiled 2054 to 1227 computations (40.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
✓	0.4b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))
✓	0.6b	(cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37))))

series1.2s (26.9%)

Counts

3 → 108

Calls

3 calls:

801.0ms

(*.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

383.0ms

(cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37))))

21.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

7.0ms

(cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37))))

5.0ms

(*.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

simplify201.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

581×	`fma-def_binary64`
328×	`times-frac_binary64`
262×	`associate-/r*_binary64`
250×	`associate-/l*_binary64`
238×	`*-commutative_binary64`

Counts

223 → 283

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	690	10556
1	1989	9753
2	4935	9490
3	4962	9490

prune698.0ms (15.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	585	0	585
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	585	4	589

Error

Counts

589 → 4

Alt Table

Status	Error	Program
▶	21.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

Compiler

Compiled 29878 to 19728 computations (34% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 d2 (+.f64 d3 37)))
✓	0.2b	(*.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
✓	0.3b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))

series88.0ms (2%)

Counts

3 → 64

Calls

3 calls:

51.0ms	(*.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
29.0ms	(sqrt.f64 (+.f64 d2 (+.f64 d3 37)))
7.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
16×	`sqrt-prod_binary64`
16×	`associate-r_binary64`
16×	`sqrt-div_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

3 → 81

Calls

3 calls:

12.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
8.0ms	(*.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
4.0ms	(sqrt.f64 (+.f64 d2 (+.f64 d3 37)))

simplify89.0ms (2%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-in_binary64`
680×	`distribute-lft-in_binary64`
605×	`fma-def_binary64`
243×	`associate-l_binary64`
192×	`associate-r_binary64`

Counts

145 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	2557
1	501	2401
2	1562	2345
3	4909	2343
4	4973	2343

prune114.0ms (2.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	199	4	203

Error

Counts

203 → 4

Alt Table

Status	Error	Program
✓	21.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

Compiler

Compiled 5054 to 3488 computations (31% saved)

regimes220.0ms (4.9%)

Accuracy

Total 0.0b remaining (78.6%)

Threshold costs 0.0b (78.6%)

Counts

47 → 1

Compiler

Compiled 3698 to 2640 computations (28.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
2	11	10

end67.0ms (1.5%)

Remove: (sort d2 d3)
Compiler: Compiled 113 to 79 computations (30.1% saved)

Details

analyze423.0ms (9.4%)

sample969.0ms (21.6%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite7.0ms (0.2%)

simplify61.0ms (1.4%)

prune34.0ms (0.8%)

localize8.0ms (0.2%)

series22.0ms (0.5%)

rewrite15.0ms (0.3%)

simplify87.0ms (1.9%)

prune67.0ms (1.5%)

localize9.0ms (0.2%)

series1.2s (26.9%)

rewrite38.0ms (0.8%)

simplify201.0ms (4.5%)

prune698.0ms (15.6%)

localize8.0ms (0.2%)

series88.0ms (2%)

rewrite30.0ms (0.7%)

simplify89.0ms (2%)

prune114.0ms (2.5%)

regimes220.0ms (4.9%)

simplify2.0ms (0%)

end67.0ms (1.5%)

Profiling