Details

analyze1.8s (25.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 44 to 32 computations (27.3% saved)

sample1.2s (16.5%)

Symmetry

(sort a b c d)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 57 to 41 computations (28.1% saved)

simplify11.0ms (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%)

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

3.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.8b	(*.f64 (+.f64 a (+.f64 b (+.f64 c d))) 2)

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(+.f64 b (+.f64 c d))
✓	2.8b	(+.f64 a (+.f64 b (+.f64 c d)))

series11.0ms (0.1%)

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:

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

simplify57.0ms (0.8%)

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 (0.7%)

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
	2.8b	(*.f64 (+.f64 a (+.f64 (+.f64 b c) d)) 2)
	3.6b	(.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)
	3.1b	(*.f64 (expm1.f64 (log1p.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 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)
	3.6b	(.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)
	4.0b	(.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)
	2.9b	(.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)
▶	1.5b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d))))) 2)
	2.6b	(*.f64 (log1p.f64 (expm1.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)

Compiler

Compiled 1467 to 625 computations (57.4% saved)

localize13.0ms (0.2%)

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 c) (exp.f64 d))
✓	0.4b	(.f64 (exp.f64 b) (.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 (24.4%)

Counts

4 → 136

Calls

4 calls:

1.7s	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))
35.0ms	(.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d))))
19.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
7.0ms	(*.f64 (exp.f64 c) (exp.f64 d))

rewrite37.0ms (0.5%)

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:

12.0ms	(.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)))))
7.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
5.0ms	(*.f64 (exp.f64 c) (exp.f64 d))

simplify112.0ms (1.6%)

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

prune81.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	207	4	211

Error

Counts

211 → 4

Alt Table

Status	Error	Program
	2.8b	(*.f64 (+.f64 a (+.f64 (+.f64 b c) 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)
	2.6b	(*.f64 (log1p.f64 (expm1.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)

Compiler

Compiled 4103 to 1499 computations (63.5% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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))

series1.2s (16.6%)

Counts

3 → 41

Calls

3 calls:

1.1s	(+.f64 c (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)))
8.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
16×	`pow1_binary64`
10×	`add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 63

Calls

3 calls:

11.0ms	(+.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))

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

104 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	1606
1	462	1237
2	1402	1167
3	4332	1167
4	5173	1167

prune77.0ms (1.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	142	2	144

Error

Counts

144 → 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 (log.f64 (exp.f64 (+.f64 b (+.f64 d a))))) 2)

Compiler

Compiled 2618 to 1030 computations (60.7% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.2%)

Counts

2 → 84

Calls

2 calls:

9.0ms	(+.f64 c (log.f64 (exp.f64 (+.f64 b (+.f64 d a)))))
6.0ms	(exp.f64 (+.f64 b (+.f64 d a)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64`
5×	`exp-prod_binary64`
5×	`distribute-lft-out_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

8.0ms	(+.f64 c (log.f64 (exp.f64 (+.f64 b (+.f64 d a)))))
7.0ms	(exp.f64 (+.f64 b (+.f64 d a)))

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Rules

557×	`distribute-rgt-in_binary64`
549×	`fma-def_binary64`
525×	`distribute-lft-in_binary64`
388×	`associate-l_binary64`
315×	`associate-r_binary64`

Counts

124 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1361
1	275	1276
2	990	1239
3	4843	1239
4	4984	1239

prune45.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	92	2	94

Error

Counts

94 → 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 (log.f64 (exp.f64 (+.f64 b (+.f64 d a))))) 2)

Compiler

Compiled 1589 to 604 computations (62% saved)

regimes403.0ms (5.7%)

Accuracy

Total 0.0b remaining (88.9%)

Threshold costs 0.0b (88.9%)

Counts

43 → 1

Compiler

Compiled 6790 to 4542 computations (33.1% 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	12	17
1	16	17
2	16	17

end62.0ms (0.9%)

Remove: (sort a b c d)
Compiler: Compiled 92 to 68 computations (26.1% saved)

Details

analyze1.8s (25.4%)

sample1.2s (16.5%)

simplify11.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series11.0ms (0.1%)

rewrite13.0ms (0.2%)

simplify57.0ms (0.8%)

prune50.0ms (0.7%)

localize13.0ms (0.2%)

series1.7s (24.4%)

rewrite37.0ms (0.5%)

simplify112.0ms (1.6%)

prune81.0ms (1.1%)

localize12.0ms (0.2%)

series1.2s (16.6%)

rewrite27.0ms (0.4%)

simplify79.0ms (1.1%)

prune77.0ms (1.1%)

localize9.0ms (0.1%)

series15.0ms (0.2%)

rewrite17.0ms (0.2%)

simplify68.0ms (1%)

prune45.0ms (0.6%)

regimes403.0ms (5.7%)

simplify2.0ms (0%)

end62.0ms (0.9%)

Profiling