Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 44 to 32 computations (27.3% saved)

sample1.0s (16.6%)

Infinites

0% of outputs are infinite.

Symmetry

(sort a b c d)

Results

951.0ms

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

3.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.7b	(*.f64 (+.f64 a (+.f64 b (+.f64 c d))) 2)

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(+.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))

rewrite13.0ms (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:

7.0ms	(+.f64 a (+.f64 b (+.f64 c d)))
4.0ms	(+.f64 b (+.f64 c d))

simplify55.0ms (0.9%)

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

prune52.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	64	10	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	10	75

Error

0.7b

Counts

75 → 10

Alt Table

Status	Error	Program
	3.6b	(.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)
▶	1.5b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d))))) 2)
	2.9b	(*.f64 (+.f64 a (+.f64 (+.f64 b c) d)) 2)
	5.4b	(.f64 (fma.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (cbrt.f64 a) (+.f64 b (+.f64 c d))) 2)
	3.9b	(.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)
	3.8b	(.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)
	3.5b	(.f64 (/.f64 (-.f64 (.f64 a a) (*.f64 (+.f64 c (+.f64 d b)) (+.f64 c (+.f64 d b)))) (-.f64 a (+.f64 c (+.f64 d b)))) 2)
	2.7b	(*.f64 (+.f64 c (+.f64 a (+.f64 d b))) 2)
	3.9b	(.f64 (.f64 (*.f64 (cbrt.f64 (+.f64 a (+.f64 b (+.f64 c d)))) (cbrt.f64 (+.f64 a (+.f64 b (+.f64 c d))))) (cbrt.f64 (+.f64 a (+.f64 b (+.f64 c d))))) 2)

Compiler

Compiled 1471 to 621 computations (57.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (exp.f64 b) (.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 c) (exp.f64 d))
✓	0.8b	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))

series1.7s (27.6%)

Counts

4 → 136

Calls

4 calls:

1.6s	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))
36.0ms	(.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d))))
23.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
8.0ms	(*.f64 (exp.f64 c) (exp.f64 d))

rewrite37.0ms (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:

11.0ms	(.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d))))
9.0ms	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))
7.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
5.0ms	(*.f64 (exp.f64 c) (exp.f64 d))

simplify123.0ms (2%)

Algorithm

1×	egg-herbie

Rules

678×	`prod-exp_binary64`
481×	`associate-r_binary64`
385×	`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

prune90.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	207	4	211

Error

0.0b

Counts

211 → 4

Alt Table

Status	Error	Program
	1.3b	(.f64 (log.f64 (.f64 (exp.f64 a) (*.f64 (exp.f64 (+.f64 b c)) (exp.f64 d)))) 2)
▶	0.1b	(.f64 (+.f64 c (log.f64 (.f64 (exp.f64 b) (*.f64 (exp.f64 d) (exp.f64 a))))) 2)
	0.2b	(.f64 (+.f64 (log.f64 (.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))) b) 2)
	2.7b	(*.f64 (+.f64 c (+.f64 a (+.f64 d b))) 2)

Compiler

Compiled 4107 to 1501 computations (63.5% 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)))))
✓	0.4b	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))
✓	0.4b	(*.f64 (exp.f64 d) (exp.f64 a))

series2.1s (34.3%)

Counts

4 → 53

Calls

4 calls:

1.1s	(+.f64 c (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))))
986.0ms	(log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a))))
17.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))
8.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

rewrite29.0ms (0.5%)

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

simplify72.0ms (1.2%)

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 → 172

Iterations

Useful iterations: 2 (0.0ms)

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

prune80.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	174	2	176

Error

Counts

176 → 2

Alt Table

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

Compiler

Compiled 3062 to 1152 computations (62.4% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

6.0ms

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

rewrite7.0ms (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:

6.0ms

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

simplify46.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

676×	`distribute-rgt-in_binary64`
650×	`distribute-lft-in_binary64`
605×	`associate--l+_binary64`
517×	`associate--r+_binary64`
392×	`associate-l_binary64`

Counts

70 → 41

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	681
1	129	660
2	531	660
3	2970	660
4	4912	660

prune18.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	42	1	43

Error

Counts

43 → 1

Alt Table

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

Compiler

Compiled 555 to 198 computations (64.3% saved)

regimes566.0ms (9.3%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

60 → 1

Compiler

Compiled 9980 to 6560 computations (34.3% 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

end44.0ms (0.7%)

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

Details

analyze4.0ms (0.1%)

sample1.0s (16.6%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series10.0ms (0.2%)

rewrite13.0ms (0.2%)

simplify55.0ms (0.9%)

prune52.0ms (0.8%)

localize13.0ms (0.2%)

series1.7s (27.6%)

rewrite37.0ms (0.6%)

simplify123.0ms (2%)

prune90.0ms (1.5%)

localize12.0ms (0.2%)

series2.1s (34.3%)

rewrite29.0ms (0.5%)

simplify72.0ms (1.2%)

prune80.0ms (1.3%)

localize7.0ms (0.1%)

series6.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify46.0ms (0.8%)

prune18.0ms (0.3%)

regimes566.0ms (9.3%)

simplify2.0ms (0%)

end44.0ms (0.7%)

Profiling