Details

analyze3.0ms (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)

sample57.0ms (1%)

Algorithm

1×

intervals

Symmetry

(sort a b c d)

Results

11.0ms	256×	pre	128	true
8.0ms	256×	body	128	valid

Compiler

Compiled 61 to 45 computations (26.2% 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

prune3.0ms (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

3.7b

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)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(+.f64 b (+.f64 c d))
✓	2.7b	(+.f64 a (+.f64 b (+.f64 c d)))

series11.0ms (0.2%)

Counts

2 → 84

Calls

2 calls:

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

rewrite12.0ms (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))

simplify58.0ms (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

prune48.0ms (0.8%)

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

0.8b

Counts

75 → 9

Alt Table

Status	Error	Program
	3.2b	(.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)
	3.8b	(.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)
	2.9b	(*.f64 (log1p.f64 (expm1.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)
	2.9b	(*.f64 (expm1.f64 (log1p.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)
	3.7b	(.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 a (+.f64 (+.f64 b 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)

Compiler

Compiled 1365 to 583 computations (57.3% 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)))
✓	0.9b	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))

series1.7s (28.2%)

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))))
17.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
7.0ms	(*.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))))
9.0ms	(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))

simplify111.0ms (1.9%)

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

prune121.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	7	1	8
Picked	0	1	1
Done	0	0	0
Total	205	5	210

Error

Counts

210 → 5

Alt Table

Status	Error	Program
✓	1.6b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.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)
	0.1b	(.f64 (+.f64 (log.f64 (.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))) b) 2)
	1.8b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 c) (exp.f64 d)) (.f64 (exp.f64 c) (exp.f64 d))) (.f64 (exp.f64 c) (exp.f64 d))))))) 2)
	2.9b	(*.f64 (log1p.f64 (expm1.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)

Compiler

Compiled 4157 to 1529 computations (63.2% saved)

localize13.0ms (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))

series1.4s (22.8%)

Counts

3 → 41

Calls

3 calls:

1.3s	(+.f64 c (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))))
31.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))
7.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

rewrite26.0ms (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)))))
7.0ms	(.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`
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

prune91.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	142	3	145

Error

Counts

145 → 3

Alt Table

Status	Error	Program
	0.1b	(.f64 (+.f64 (log.f64 (.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))) b) 2)
✓	1.6b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d))))) 2)
▶	0.0b	(*.f64 (+.f64 c (log.f64 (exp.f64 (+.f64 b (+.f64 d a))))) 2)

Compiler

Compiled 2636 to 1044 computations (60.4% saved)

localize12.0ms (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)))))

series14.0ms (0.2%)

Counts

2 → 84

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)))

rewrite17.0ms (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:

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

simplify75.0ms (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

prune47.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	92	3	95

Error

Counts

95 → 3

Alt Table

Status	Error	Program
	0.1b	(.f64 (+.f64 (log.f64 (.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))) b) 2)
✓	1.6b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d))))) 2)
✓	0.0b	(*.f64 (+.f64 c (log.f64 (exp.f64 (+.f64 b (+.f64 d a))))) 2)

Compiler

Compiled 1607 to 618 computations (61.5% saved)

regimes864.0ms (14.6%)

Accuracy

Total 0.0b remaining (93.2%)

Threshold costs 0.0b (93.2%)

Counts

78 → 1

Compiler

Compiled 13565 to 8901 computations (34.4% saved)

simplify3.0ms (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

end14.0ms (0.2%)

Remove: (sort a b c d)
Compiler: Compiled 45 to 33 computations (26.7% saved)

sample1.2s (19.7%)

Algorithm

1×

intervals

Results

483.0ms	8000×	pre	128	true
270.0ms	8000×	body	128	valid

Compiler

Compiled 113 to 85 computations (24.8% saved)

Details

analyze3.0ms (0%)

sample57.0ms (1%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series11.0ms (0.2%)

rewrite12.0ms (0.2%)

simplify58.0ms (1%)

prune48.0ms (0.8%)

localize13.0ms (0.2%)

series1.7s (28.2%)

rewrite39.0ms (0.7%)

simplify111.0ms (1.9%)

prune121.0ms (2%)

localize13.0ms (0.2%)

series1.4s (22.8%)

rewrite26.0ms (0.4%)

simplify72.0ms (1.2%)

prune91.0ms (1.5%)

localize12.0ms (0.2%)

series14.0ms (0.2%)

rewrite17.0ms (0.3%)

simplify75.0ms (1.3%)

prune47.0ms (0.8%)

regimes864.0ms (14.6%)

simplify3.0ms (0%)

end14.0ms (0.2%)

sample1.2s (19.7%)

Profiling