Details

analyze1.4s (23.9%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.1%	0.9%	9
0%	98.1%	1.9%	10
0%	95.6%	4.4%	11
0%	94.5%	5.5%	12
0%	93.4%	6.6%	13
0%	92.7%	7.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.7s (29.3%)

Symmetry

(sort d2 d3)

Results

888.0ms	7752×	body	128	valid
578.0ms	1044×	body	8192	exit
78.0ms	159×	body	1024	valid
59.0ms	343×	body	128	invalid
48.0ms	205×	body	512	valid
27.0ms	140×	body	256	valid

Compiler

Compiled 29 to 19 computations (34.5% saved)

simplify7.0ms (0.1%)

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

prune31.0ms (0.5%)

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 d1 (+.f64 3 (+.f64 d2 d3)))
	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 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 (0.1%)

Counts

1 → 28

Calls

1 calls:

8.0ms

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

rewrite9.0ms (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:

8.0ms

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

simplify69.0ms (1.2%)

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

prune40.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	44	6	50

Error

Counts

50 → 6

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	21.6b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.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))))
	31.8b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
	24.9b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	51.2b	(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)))))

Compiler

Compiled 831 to 463 computations (44.3% 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)))))
✓	0.4b	(.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))))
✓	0.4b	(cbrt.f64 (+.f64 3 (+.f64 d2 d3)))
✓	0.4b	(*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))

series702.0ms (12%)

Counts

4 → 120

Calls

4 calls:

574.0ms	(.f64 d1 (.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3)))))
78.0ms	(*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
41.0ms	(cbrt.f64 (+.f64 3 (+.f64 d2 d3)))
9.0ms	(.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))))

rewrite87.0ms (1.5%)

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:

21.0ms	(.f64 d1 (.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3)))))
19.0ms	(.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))))
11.0ms	(*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
5.0ms	(cbrt.f64 (+.f64 3 (+.f64 d2 d3)))

simplify229.0ms (3.9%)

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 → 355

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	755	11339
1	2310	10560
2	4992	10558
3	5180	10558

prune563.0ms (9.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	500	1	501
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	501	6	507

Error

Counts

507 → 6

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	21.6b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.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))))
	31.8b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
	24.9b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
▶	0.1b	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))

Compiler

Compiled 24283 to 16125 computations (33.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series16.0ms (0.3%)

Counts

2 → 54

Calls

2 calls:

9.0ms	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))
6.0ms	(+.f64 (.f64 d1 d3) (.f64 3 d1))

rewrite9.0ms (0.1%)

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))

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

84 → 63

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

prune46.0ms (0.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	63	6	69

Error

Counts

69 → 6

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
▶	21.6b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.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))))
	31.8b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
	24.9b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
✓	0.1b	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))

Compiler

Compiled 1122 to 576 computations (48.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 3 (+.f64 d2 d3)))
✓	0.2b	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.2b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

series103.0ms (1.8%)

Counts

3 → 60

Calls

3 calls:

62.0ms	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
33.0ms	(sqrt.f64 (+.f64 3 (+.f64 d2 d3)))
8.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

rewrite31.0ms (0.5%)

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:

15.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
7.0ms	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
4.0ms	(sqrt.f64 (+.f64 3 (+.f64 d2 d3)))

simplify142.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

644×	`fma-def_binary64`
436×	`fma-neg_binary64`
421×	`*-commutative_binary64`
307×	`cancel-sign-sub-inv_binary64`
244×	`associate-l_binary64`

Counts

141 → 133

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	195	2457
1	510	2313
2	1664	2269
3	3116	2260
4	4816	2258
5	4998	2258
6	4950	2258

prune122.0ms (2.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	168	6	174

Error

Counts

174 → 6

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
✓	21.6b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.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))))
	31.8b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
	24.9b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
✓	0.1b	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))

Compiler

Compiled 4440 to 2728 computations (38.6% saved)

regimes346.0ms (5.9%)

Accuracy

Total 0.1b remaining (86.7%)

Threshold costs 0.1b (86.7%)

Counts

73 → 1

Compiler

Compiled 5324 to 3684 computations (30.8% 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

end82.0ms (1.4%)

Remove: (sort d2 d3)
Compiler: Compiled 141 to 92 computations (34.8% saved)

Details

analyze1.4s (23.9%)

sample1.7s (29.3%)

simplify7.0ms (0.1%)

prune31.0ms (0.5%)

localize5.0ms (0.1%)

series8.0ms (0.1%)

rewrite9.0ms (0.2%)

simplify69.0ms (1.2%)

prune40.0ms (0.7%)

localize9.0ms (0.2%)

series702.0ms (12%)

rewrite87.0ms (1.5%)

simplify229.0ms (3.9%)

prune563.0ms (9.6%)

localize7.0ms (0.1%)

series16.0ms (0.3%)

rewrite9.0ms (0.1%)

simplify69.0ms (1.2%)

prune46.0ms (0.8%)

localize8.0ms (0.1%)

series103.0ms (1.8%)

rewrite31.0ms (0.5%)

simplify142.0ms (2.4%)

prune122.0ms (2.1%)

regimes346.0ms (5.9%)

simplify2.0ms (0%)

end82.0ms (1.4%)

Profiling