Details

analyze704.0ms (17.6%)

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
37.4%	62.4%	0.1%	8
40.6%	57.7%	1.7%	9
45.2%	51.1%	3.7%	10
57.7%	33.5%	8.7%	11
59.7%	29.4%	10.9%	12
62%	25%	13%	13
68.3%	17.4%	14.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample30.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	237×	body	128	valid
1.0ms	9×	body	1024	valid
1.0ms	9×	body	512	valid
1.0ms	23×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`distribute-lft-out_binary64`
6×	`associate-+r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	10
2	44	10
3	64	10
4	66	10
5	67	10
6	67	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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
▶	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 69 to 45 computations (34.8% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

series8.0ms (0.2%)

Counts

1 → 28

Calls

1 calls:

8.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

rewrite8.0ms (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 3 (+.f64 d2 d3)))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

949×	`distribute-rgt-in_binary64`
943×	`distribute-lft-in_binary64`
503×	`fma-neg_binary64`
394×	`associate-l_binary64`
294×	`associate-r_binary64`

Counts

54 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	601
1	162	559
2	683	559
3	2795	559
4	3172	559
5	4459	559
6	4975	559

prune36.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	45	5	50

Error

Counts

50 → 5

Alt Table

Status	Error	Program
	26.0b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	32.3b	(/.f64 (.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))) (+.f64 (.f64 3 3) (-.f64 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)) (.f64 3 (+.f64 d2 d3)))))
	51.8b	(cbrt.f64 (.f64 (.f64 (.f64 d1 d1) d1) (.f64 (*.f64 (+.f64 3 (+.f64 d2 d3)) (+.f64 3 (+.f64 d2 d3))) (+.f64 3 (+.f64 d2 d3)))))
▶	1.1b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 827 to 457 computations (44.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 d1 (.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3)))))
✓	0.3b	(*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.4b	(cbrt.f64 (+.f64 3 (+.f64 d2 d3)))
✓	0.4b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))

series681.0ms (17%)

Counts

4 → 120

Calls

4 calls:

559.0ms	(.f64 d1 (.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3)))))
76.0ms	(*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
33.0ms	(cbrt.f64 (+.f64 3 (+.f64 d2 d3)))
12.0ms	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))

rewrite73.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
70×	`*-un-lft-identity_binary64`
46×	`cbrt-prod_binary64`
44×	`associate-*r/_binary64`
40×	`flip-+_binary64`

Counts

4 → 162

Calls

4 calls:

23.0ms	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
12.0ms	(.f64 d1 (.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3)))))
12.0ms	(*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
4.0ms	(cbrt.f64 (+.f64 3 (+.f64 d2 d3)))

simplify224.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
319×	`*-commutative_binary64`
236×	`fma-neg_binary64`
226×	`associate--l+_binary64`
173×	`+-commutative_binary64`

Counts

282 → 318

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	755	11313
1	2310	10560
2	4992	10558
3	5180	10558

prune481.0ms (12%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	444	2	446
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	446	5	451

Error

Counts

451 → 5

Alt Table

Status	Error	Program
	26.0b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	32.3b	(/.f64 (*.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))) (fma.f64 (+.f64 d2 d3) (+.f64 (+.f64 d2 d3) -3) 9))
✓	1.1b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
▶	0.1b	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 22657 to 15174 computations (33% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))
✓	0.0b	(+.f64 (.f64 d1 d3) (.f64 3 d1))

series14.0ms (0.4%)

Counts

2 → 54

Calls

2 calls:

9.0ms	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))
5.0ms	(+.f64 (.f64 d1 d3) (.f64 3 d1))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
4×	`sum-log_binary64`
2×	`+-commutative_binary64`
2×	`flip-+_binary64`
2×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

5.0ms	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))
3.0ms	(+.f64 (.f64 d1 d3) (.f64 3 d1))

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-neg_binary64`
637×	`associate-l_binary64`
555×	`fma-def_binary64`
507×	`associate-r_binary64`
421×	`distribute-rgt-in_binary64`

Counts

84 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	876
1	236	834
2	889	826
3	3670	822
4	4612	822
5	5002	822

prune41.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	62	5	67

Error

Counts

67 → 5

Alt Table

Status	Error	Program
▶	26.0b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	32.3b	(/.f64 (*.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))) (fma.f64 (+.f64 d2 d3) (+.f64 (+.f64 d2 d3) -3) 9))
✓	1.1b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.1b	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 1103 to 560 computations (49.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
✓	7.8b	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
✓	16.7b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

series106.0ms (2.7%)

Counts

3 → 96

Calls

3 calls:

66.0ms	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
34.0ms	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
6.0ms	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`

Counts

3 → 108

Calls

3 calls:

9.0ms	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
7.0ms	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
5.0ms	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))

simplify112.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

245×	`fma-neg_binary64`
237×	`associate-/l*_binary64`
236×	`associate-r_binary64`
218×	`associate-l_binary64`
196×	`times-frac_binary64`

Counts

204 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	5107
1	958	4615
2	4155	4506
3	4970	4506

prune143.0ms (3.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	204	5	209

Error

Counts

209 → 5

Alt Table

Status	Error	Program
✓	26.0b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	23.6b	(/.f64 d1 (/.f64 (-.f64 3 (+.f64 d2 d3)) (-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3)))))
✓	1.1b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.1b	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 6082 to 2874 computations (52.7% saved)

regimes406.0ms (10.1%)

Accuracy

Total 0.1b remaining (92.6%)

Threshold costs 0.1b (92.6%)

Counts

85 → 1

Compiler

Compiled 6248 to 4260 computations (31.8% saved)

simplify4.0ms (0.1%)

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

end6.0ms (0.2%)

Remove: (sort d2 d3)
Compiler: Compiled 30 to 21 computations (30% saved)

sample706.0ms (17.6%)

Algorithm

1×

intervals

Results

301.0ms	7513×	body	128	valid
24.0ms	645×	body	128	invalid
22.0ms	151×	body	1024	valid
21.0ms	201×	body	512	valid
10.0ms	135×	body	256	valid

Compiler

Compiled 117 to 74 computations (36.8% saved)

Details

analyze704.0ms (17.6%)

sample30.0ms (0.7%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series8.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify67.0ms (1.7%)

prune36.0ms (0.9%)

localize9.0ms (0.2%)

series681.0ms (17%)

rewrite73.0ms (1.8%)

simplify224.0ms (5.6%)

prune481.0ms (12%)

localize7.0ms (0.2%)

series14.0ms (0.4%)

rewrite11.0ms (0.3%)

simplify76.0ms (1.9%)

prune41.0ms (1%)

localize8.0ms (0.2%)

series106.0ms (2.7%)

rewrite28.0ms (0.7%)

simplify112.0ms (2.8%)

prune143.0ms (3.6%)

regimes406.0ms (10.1%)

simplify4.0ms (0.1%)

end6.0ms (0.2%)

sample706.0ms (17.6%)

Profiling