Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 44 to 32 computations (27.3% saved)

sample1.1s (19.6%)

Symmetry

(sort a b c d)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 101 to 73 computations (27.7% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

114×	`fma-def_binary64`
49×	`distribute-rgt-in_binary64`
46×	`distribute-lft-in_binary64`
40×	`associate-+l+_binary64`
32×	`associate-+r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	52	13
3	124	13
4	193	13
5	245	13
6	247	13
7	236	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

3.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.5b	(*.f64 (+.f64 a (+.f64 b (+.f64 c d))) 2)

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(+.f64 b (+.f64 c d))
✓	2.9b	(+.f64 a (+.f64 b (+.f64 c d)))

series10.0ms (0.2%)

Counts

2 → 84

Calls

2 calls:

6.0ms	(+.f64 a (+.f64 b (+.f64 c d)))
4.0ms	(+.f64 b (+.f64 c d))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
16×	`add-log-exp_binary64`
9×	`distribute-lft-out_binary64`
9×	`sum-log_binary64`
6×	`fma-def_binary64`

Counts

2 → 42

Calls

2 calls:

6.0ms	(+.f64 a (+.f64 b (+.f64 c d)))
4.0ms	(+.f64 b (+.f64 c d))

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Rules

791×	`associate--l+_binary64`
721×	`distribute-rgt-in_binary64`
666×	`distribute-lft-in_binary64`
390×	`associate-l_binary64`
261×	`fma-def_binary64`

Counts

126 → 74

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	67	1070
1	198	1049
2	692	1049
3	3441	1049
4	5208	1049

prune45.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	66	8	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	8	75

Error

0.8b

Counts

75 → 8

Alt Table

Status	Error	Program
	5.9b	(.f64 (fma.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (cbrt.f64 a) (+.f64 b (+.f64 c d))) 2)
	2.9b	(*.f64 (+.f64 a (+.f64 (+.f64 b c) d)) 2)
	2.7b	(*.f64 (+.f64 c (+.f64 a (+.f64 d b))) 2)
	4.0b	(.f64 (/.f64 (-.f64 (.f64 a a) (*.f64 (+.f64 b (+.f64 c d)) (+.f64 b (+.f64 c d)))) (-.f64 a (+.f64 b (+.f64 c d)))) 2)
	3.5b	(.f64 (/.f64 (+.f64 (pow.f64 a 3) (pow.f64 (+.f64 c (+.f64 d b)) 3)) (fma.f64 (+.f64 c (+.f64 d b)) (-.f64 (+.f64 c (+.f64 d b)) a) (.f64 a a))) 2)
	3.9b	(.f64 (/.f64 (+.f64 (pow.f64 a 3) (pow.f64 (+.f64 b (+.f64 c d)) 3)) (+.f64 (.f64 a a) (-.f64 (.f64 (+.f64 b (+.f64 c d)) (+.f64 b (+.f64 c d))) (.f64 a (+.f64 b (+.f64 c d)))))) 2)
	3.7b	(.f64 (log.f64 (.f64 (exp.f64 a) (*.f64 (exp.f64 b) (exp.f64 (+.f64 c d))))) 2)
▶	1.7b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d))))) 2)

Compiler

Compiled 1349 to 571 computations (57.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (exp.f64 c) (exp.f64 d))
✓	0.4b	(.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d))))
✓	0.4b	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
✓	1.0b	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))

series1.5s (26.9%)

Counts

4 → 136

Calls

4 calls:

1.5s	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))
33.0ms	(.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d))))
16.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
6.0ms	(*.f64 (exp.f64 c) (exp.f64 d))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
21×	`*-un-lft-identity_binary64`
20×	`add-cbrt-cube_binary64`
16×	`prod-exp_binary64`
16×	`pow-prod-down_binary64`

Counts

4 → 85

Calls

4 calls:

10.0ms	(.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d))))
8.0ms	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))
6.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
5.0ms	(*.f64 (exp.f64 c) (exp.f64 d))

simplify114.0ms (2%)

Algorithm

1×	egg-herbie

Rules

678×	`prod-exp_binary64`
481×	`associate-r_binary64`
386×	`distribute-rgt-out_binary64`
366×	`associate-l_binary64`
267×	`associate-+l+_binary64`

Counts

221 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	3683
1	693	2727
2	2359	2617
3	4148	2617
4	5037	2617

prune88.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	197	4	201
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	202	7	209

Error

0.0b

Counts

209 → 7

Alt Table

Status	Error	Program
	2.9b	(*.f64 (+.f64 a (+.f64 (+.f64 b c) d)) 2)
	4.2b	(.f64 (log.f64 (.f64 (exp.f64 a) (*.f64 (exp.f64 b) (expm1.f64 (log1p.f64 (exp.f64 (+.f64 c d))))))) 2)
	2.7b	(*.f64 (+.f64 c (+.f64 a (+.f64 d b))) 2)
▶	0.2b	(.f64 (+.f64 c (log.f64 (.f64 (exp.f64 b) (*.f64 (exp.f64 d) (exp.f64 a))))) 2)
	1.6b	(.f64 (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (.f64 (exp.f64 c) (exp.f64 a))))) 2)
	0.2b	(.f64 (+.f64 (log.f64 (.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))) b) 2)
✓	1.7b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d))))) 2)

Compiler

Compiled 4191 to 1567 computations (62.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a))))
✓	0.0b	(+.f64 c (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))))
✓	0.3b	(*.f64 (exp.f64 d) (exp.f64 a))
✓	0.4b	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))

series2.0s (35.3%)

Counts

4 → 53

Calls

4 calls:

1.0s	(+.f64 c (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))))
953.0ms	(log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a))))
16.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))
6.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary64`
21×	`*-un-lft-identity_binary64`
11×	`add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`pow-prod-down_binary64`

Counts

4 → 80

Calls

4 calls:

9.0ms	(log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a))))
8.0ms	(+.f64 c (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))))
8.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))
5.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-def_binary64`
557×	`prod-exp_binary64`
416×	`distribute-rgt-in_binary64`
409×	`*-commutative_binary64`
405×	`distribute-lft-in_binary64`

Counts

133 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	1915
1	470	1432
2	1416	1362
3	4394	1362
4	5126	1362

prune83.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	3	2	5
Picked	1	0	1
Done	1	0	1
Total	175	3	178

Error

Counts

178 → 3

Alt Table

Status	Error	Program
	2.9b	(*.f64 (+.f64 a (+.f64 (+.f64 b c) d)) 2)
▶	0.0b	(*.f64 (+.f64 c (+.f64 b (+.f64 d a))) 2)
	0.2b	(.f64 (+.f64 (log.f64 (.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))) b) 2)

Compiler

Compiled 3083 to 1165 computations (62.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 c (+.f64 b (+.f64 d a)))

series6.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

6.0ms

(+.f64 c (+.f64 b (+.f64 d a)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
6×	`distribute-lft-out_binary64`
6×	`sum-log_binary64`
3×	`fma-def_binary64`

Counts

1 → 22

Calls

1 calls:

7.0ms

(+.f64 c (+.f64 b (+.f64 d a)))

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Rules

540×	`distribute-rgt-in_binary64`
529×	`associate--l+_binary64`
517×	`associate--r+_binary64`
516×	`distribute-lft-in_binary64`
412×	`distribute-neg-in_binary64`

Counts

70 → 41

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	681
1	128	660
2	470	660
3	2504	660
4	4595	660
5	5020	660

prune18.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	43	1	44

Error

Counts

44 → 1

Alt Table

Status	Error	Program
	0b	(*.f64 (+.f64 (+.f64 c b) (+.f64 d a)) 2)

Compiler

Compiled 555 to 199 computations (64.1% saved)

regimes305.0ms (5.3%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

35 → 1

Compiler

Compiled 5804 to 3784 computations (34.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	14	13

end45.0ms (0.8%)

Remove: (sort a b c d)
Compiler: Compiled 65 to 45 computations (30.8% saved)

Details

analyze2.0ms (0%)

sample1.1s (19.6%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize9.0ms (0.2%)

series10.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify59.0ms (1%)

prune45.0ms (0.8%)

localize13.0ms (0.2%)

series1.5s (26.9%)

rewrite33.0ms (0.6%)

simplify114.0ms (2%)

prune88.0ms (1.5%)

localize12.0ms (0.2%)

series2.0s (35.3%)

rewrite32.0ms (0.6%)

simplify75.0ms (1.3%)

prune83.0ms (1.4%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite8.0ms (0.1%)

simplify56.0ms (1%)

prune18.0ms (0.3%)

regimes305.0ms (5.3%)

simplify2.0ms (0%)

end45.0ms (0.8%)

Profiling