Details

analyze377.0ms (13.2%)

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)

sample43.0ms (1.5%)

Algorithm

1×

intervals

Symmetry

(sort d2 d3)

Results

10.0ms	245×	body	128	valid
1.0ms	27×	body	128	invalid
1.0ms	6×	body	512	valid
0.0ms	4×	body	256	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify7.0ms (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

0.0b

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)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.3%)

Counts

1 → 28

Calls

1 calls:

7.0ms

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

rewrite8.0ms (0.3%)

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:

7.0ms

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

simplify68.0ms (2.4%)

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

prune30.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	46	4	50

Error

0.0b

Counts

50 → 4

Alt Table

Status	Error	Program
	53.6b	(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)))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
▶	21.2b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
	23.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 753 to 413 computations (45.2% saved)

localize6.0ms (0.2%)

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))))
✓	0.3b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

series102.0ms (3.6%)

Counts

3 → 60

Calls

3 calls:

58.0ms	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
35.0ms	(sqrt.f64 (+.f64 3 (+.f64 d2 d3)))
9.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

rewrite29.0ms (1%)

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 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)))

simplify124.0ms (4.3%)

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

prune112.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	168	4	172

Error

Counts

172 → 4

Alt Table

Status	Error	Program
	21.7b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (fma.f64 1/2 (*.f64 d2 (sqrt.f64 (/.f64 1 (+.f64 3 d3)))) (sqrt.f64 (+.f64 3 d3))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
▶	0.1b	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))
	23.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 4469 to 2751 computations (38.4% saved)

localize6.0ms (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 (0.5%)

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))

rewrite8.0ms (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))

simplify69.0ms (2.4%)

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

prune37.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	62	4	66

Error

Counts

66 → 4

Alt Table

Status	Error	Program
▶	21.7b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (fma.f64 1/2 (*.f64 d2 (sqrt.f64 (/.f64 1 (+.f64 3 d3)))) (sqrt.f64 (+.f64 3 d3))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
✓	0.1b	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))
	23.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 1084 to 556 computations (48.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 1 (+.f64 3 d3)))
	0.2b	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.3b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (fma.f64 1/2 (*.f64 d2 (sqrt.f64 (/.f64 1 (+.f64 3 d3)))) (sqrt.f64 (+.f64 3 d3))))
✓	0.3b	(*.f64 d2 (sqrt.f64 (/.f64 1 (+.f64 3 d3))))

series237.0ms (8.3%)

Counts

3 → 28

Calls

3 calls:

201.0ms

(*.f64 (*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (fma.f64 1/2 (*.f64 d2 (sqrt.f64 (/.f64 1 (+.f64 3 d3)))) (sqrt.f64 (+.f64 3 d3))))

25.0ms

(*.f64 d2 (sqrt.f64 (/.f64 1 (+.f64 3 d3))))

11.0ms

(sqrt.f64 (/.f64 1 (+.f64 3 d3)))

rewrite27.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`sqrt-prod_binary64`
36×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
24×	`associate-r_binary64`

Counts

3 → 101

Calls

3 calls:

9.0ms

(*.f64 (*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (fma.f64 1/2 (*.f64 d2 (sqrt.f64 (/.f64 1 (+.f64 3 d3)))) (sqrt.f64 (+.f64 3 d3))))

8.0ms

(*.f64 d2 (sqrt.f64 (/.f64 1 (+.f64 3 d3))))

4.0ms

(sqrt.f64 (/.f64 1 (+.f64 3 d3)))

simplify126.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

384×	`associate-l_binary64`
368×	`associate-r_binary64`
332×	`fma-def_binary64`
285×	`*-commutative_binary64`
197×	`associate-+r+_binary64`

Counts

129 → 178

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	391	4131
1	1133	3883
2	4476	3883
3	4882	3883
4	4962	3883

prune196.0ms (6.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	224	4	228

Error

Counts

228 → 4

Alt Table

Status	Error	Program
✓	21.7b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (fma.f64 1/2 (*.f64 d2 (sqrt.f64 (/.f64 1 (+.f64 3 d3)))) (sqrt.f64 (+.f64 3 d3))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
✓	0.1b	(+.f64 (.f64 d2 d1) (+.f64 (.f64 d1 d3) (*.f64 3 d1)))
	23.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 8773 to 6379 computations (27.3% saved)

regimes420.0ms (14.7%)

Accuracy

Total 0.0b remaining (76%)

Threshold costs 0.0b (76%)

Counts

86 → 1

Compiler

Compiled 6504 to 4548 computations (30.1% saved)

simplify2.0ms (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)

sample776.0ms (27.1%)

Algorithm

1×

intervals

Results

363.0ms	7506×	body	128	valid
29.0ms	695×	body	128	invalid
21.0ms	157×	body	1024	valid
19.0ms	187×	body	512	valid
11.0ms	150×	body	256	valid

Compiler

Compiled 98 to 67 computations (31.6% saved)

Details

analyze377.0ms (13.2%)

sample43.0ms (1.5%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite8.0ms (0.3%)

simplify68.0ms (2.4%)

prune30.0ms (1.1%)

localize6.0ms (0.2%)

series102.0ms (3.6%)

rewrite29.0ms (1%)

simplify124.0ms (4.3%)

prune112.0ms (3.9%)

localize6.0ms (0.2%)

series14.0ms (0.5%)

rewrite8.0ms (0.3%)

simplify69.0ms (2.4%)

prune37.0ms (1.3%)

localize13.0ms (0.4%)

series237.0ms (8.3%)

rewrite27.0ms (1%)

simplify126.0ms (4.4%)

prune196.0ms (6.9%)

regimes420.0ms (14.7%)

simplify2.0ms (0.1%)

end6.0ms (0.2%)

sample776.0ms (27.1%)

Profiling