Details

analyze2.0ms (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)

sample1.1s (28.1%)

Symmetry

(sort a b c d)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 101 to 73 computations (27.7% saved)

simplify9.0ms (0.2%)

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 (0.1%)

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

3.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.6b	(*.f64 (+.f64 a (+.f64 b (+.f64 c d))) 2)

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(+.f64 b (+.f64 c d))
✓	2.7b	(+.f64 a (+.f64 b (+.f64 c d)))

series10.0ms (0.3%)

Counts

2 → 84

Calls

2 calls:

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

rewrite13.0ms (0.3%)

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)))
5.0ms	(+.f64 b (+.f64 c d))

simplify55.0ms (1.4%)

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

prune50.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	63	11	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	11	75

Error

0.7b

Counts

75 → 11

Alt Table

Status	Error	Program
	2.9b	(*.f64 (log1p.f64 (expm1.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)
	3.4b	(*.f64 (expm1.f64 (log1p.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)
	2.7b	(*.f64 (+.f64 a (+.f64 (+.f64 b 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)
	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)
	3.4b	(.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)
	3.1b	(.f64 (.f64 (*.f64 (cbrt.f64 (+.f64 c (+.f64 (+.f64 d b) a))) (cbrt.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) (cbrt.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)
	3.7b	(.f64 (log.f64 (.f64 (exp.f64 a) (*.f64 (exp.f64 b) (exp.f64 (+.f64 c d))))) 2)
▶	1.6b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d))))) 2)
	5.9b	(.f64 (fma.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (cbrt.f64 a) (+.f64 b (+.f64 c d))) 2)

Compiler

Compiled 1505 to 647 computations (57% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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)))
✓	0.4b	(*.f64 (exp.f64 c) (exp.f64 d))
✓	0.9b	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))

series1.7s (43.1%)

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)))))
34.0ms	(.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d))))
17.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
6.0ms	(*.f64 (exp.f64 c) (exp.f64 d))

rewrite39.0ms (1%)

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

simplify110.0ms (2.8%)

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

prune87.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	197	4	201
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	206	6	212

Error

0.0b

Counts

212 → 6

Alt Table

Status	Error	Program
	1.4b	(.f64 (log.f64 (.f64 (exp.f64 a) (*.f64 (exp.f64 (+.f64 b c)) (exp.f64 d)))) 2)
	2.7b	(*.f64 (+.f64 a (+.f64 (+.f64 b c) d)) 2)
	2.9b	(*.f64 (log1p.f64 (expm1.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)
	2.0b	(.f64 (.f64 (.f64 (cbrt.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))))) (cbrt.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d))))))) (cbrt.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d))))))) 2)
	0.2b	(.f64 (+.f64 c (log.f64 (.f64 (exp.f64 b) (*.f64 (exp.f64 d) (exp.f64 a))))) 2)
▶	0.1b	(.f64 (+.f64 (log.f64 (.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))) b) 2)

Compiler

Compiled 4237 to 1557 computations (63.3% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series24.0ms (0.6%)

Counts

2 → 28

Calls

2 calls:

18.0ms	(.f64 (exp.f64 c) (.f64 (exp.f64 d) (exp.f64 a)))
6.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 42

Calls

2 calls:

7.0ms	(.f64 (exp.f64 c) (.f64 (exp.f64 d) (exp.f64 a)))
5.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

simplify98.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

953×	`prod-exp_binary64`
743×	`fma-def_binary64`
443×	`associate-+l+_binary64`
410×	`*-commutative_binary64`
343×	`distribute-rgt-out_binary64`

Counts

70 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1025
1	366	844
2	1179	778
3	2669	764
4	3672	764
5	4889	764
6	5239	764

prune55.0ms (1.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	105	1	106

Error

Counts

106 → 1

Alt Table

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

Compiler

Compiled 1898 to 818 computations (56.9% saved)

localize10.0ms (0.3%)

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Error

Counts

1 → 1

Alt Table

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes439.0ms (11.4%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

41 → 1

Compiler

Compiled 6820 to 4408 computations (35.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	16	17
2	16	17

end61.0ms (1.6%)

Remove: (sort a b c d)
Compiler: Compiled 75 to 55 computations (26.7% saved)

Details

analyze2.0ms (0.1%)

sample1.1s (28.1%)

simplify9.0ms (0.2%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

series10.0ms (0.3%)

rewrite13.0ms (0.3%)

simplify55.0ms (1.4%)

prune50.0ms (1.3%)

localize13.0ms (0.3%)

series1.7s (43.1%)

rewrite39.0ms (1%)

simplify110.0ms (2.8%)

prune87.0ms (2.3%)

localize11.0ms (0.3%)

series24.0ms (0.6%)

rewrite13.0ms (0.3%)

simplify98.0ms (2.5%)

prune55.0ms (1.4%)

localize10.0ms (0.3%)

prune1.0ms (0%)

regimes439.0ms (11.4%)

simplify3.0ms (0.1%)

end61.0ms (1.6%)

Profiling