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 (21.2%)

Symmetry

(sort a b c d)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 101 to 73 computations (27.7% saved)

simplify9.0ms (0.2%)

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)

localize12.0ms (0.2%)

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)))

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))

rewrite16.0ms (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)))
4.0ms	(+.f64 b (+.f64 c d))

simplify54.0ms (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

prune46.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	65	9	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	9	75

Error

0.7b

Counts

75 → 9

Alt Table

Status	Error	Program
	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)
	2.8b	(*.f64 (+.f64 a (+.f64 (+.f64 b c) d)) 2)
	3.3b	(.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)
	3.0b	(.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)
	3.9b	(.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)
	5.9b	(.f64 (fma.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (cbrt.f64 a) (+.f64 b (+.f64 c d))) 2)
	2.7b	(*.f64 (+.f64 c (+.f64 a (+.f64 d b))) 2)

Compiler

Compiled 1413 to 595 computations (57.9% 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))
✓	0.9b	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))

series1.6s (31%)

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)))))
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)))
8.0ms	(*.f64 (exp.f64 c) (exp.f64 d))

rewrite39.0ms (0.7%)

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)))))
9.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
5.0ms	(*.f64 (exp.f64 c) (exp.f64 d))

simplify106.0ms (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 (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	207	3	210

Error

Counts

210 → 3

Alt Table

Status	Error	Program
	1.7b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (sqrt.f64 (.f64 (exp.f64 c) (exp.f64 d))) (sqrt.f64 (.f64 (exp.f64 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)

Compiler

Compiled 4099 to 1489 computations (63.7% 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 d) (exp.f64 a))
✓	0.4b	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))

series1.1s (19.9%)

Counts

3 → 41

Calls

3 calls:

1.0s	(+.f64 c (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))))
19.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))
10.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

rewrite33.0ms (0.6%)

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:

17.0ms	(+.f64 c (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))))
7.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))
5.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

simplify77.0ms (1.5%)

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 → 138

Iterations

Useful iterations: 2 (0.0ms)

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

prune67.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	139	2	141

Error

Counts

141 → 2

Alt Table

Status	Error	Program
	1.0b	(.f64 (+.f64 (+.f64 b c) (log.f64 (.f64 (exp.f64 d) (exp.f64 a)))) 2)
▶	0.0b	(*.f64 (+.f64 c (log.f64 (exp.f64 (+.f64 b (+.f64 d a))))) 2)

Compiler

Compiled 2590 to 1013 computations (60.9% saved)

localize11.0ms (0.2%)

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)))))

series13.0ms (0.3%)

Counts

2 → 84

Calls

2 calls:

7.0ms	(+.f64 c (log.f64 (exp.f64 (+.f64 b (+.f64 d a)))))
6.0ms	(exp.f64 (+.f64 b (+.f64 d a)))

rewrite15.0ms (0.3%)

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)))))
5.0ms	(exp.f64 (+.f64 b (+.f64 d a)))

simplify70.0ms (1.3%)

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

prune40.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	92	2	94

Error

Counts

94 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 c (log.f64 (exp.f64 (+.f64 b (+.f64 d a))))) 2)
	0.5b	(*.f64 (+.f64 (+.f64 b c) (log.f64 (exp.f64 (+.f64 d a)))) 2)

Compiler

Compiled 1587 to 602 computations (62.1% saved)

regimes684.0ms (12.9%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Counts

74 → 1

Compiler

Compiled 11955 to 8263 computations (30.9% 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

end56.0ms (1.1%)

Remove: (sort a b c d)
Compiler: Compiled 90 to 66 computations (26.7% saved)

Details

analyze2.0ms (0%)

sample1.1s (21.2%)

simplify9.0ms (0.2%)

prune2.0ms (0%)

localize12.0ms (0.2%)

series10.0ms (0.2%)

rewrite16.0ms (0.3%)

simplify54.0ms (1%)

prune46.0ms (0.9%)

localize13.0ms (0.2%)

series1.6s (31%)

rewrite39.0ms (0.7%)

simplify106.0ms (2%)

prune90.0ms (1.7%)

localize12.0ms (0.2%)

series1.1s (19.9%)

rewrite33.0ms (0.6%)

simplify77.0ms (1.5%)

prune67.0ms (1.3%)

localize11.0ms (0.2%)

series13.0ms (0.3%)

rewrite15.0ms (0.3%)

simplify70.0ms (1.3%)

prune40.0ms (0.8%)

regimes684.0ms (12.9%)

simplify2.0ms (0%)

end56.0ms (1.1%)

Profiling