Details

analyze1.9s (29.9%)

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 53 to 38 computations (28.3% saved)

sample1.3s (19.5%)

Symmetry

(sort a b c d e)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 120 to 85 computations (29.2% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

128×	`associate-+l+_binary64`
99×	`associate-+r+_binary64`
56×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	56	13
3	143	13
4	188	13
5	186	13
6	186	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

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (+.f64 e d) c)
✓	0.2b	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
✓	0.2b	(+.f64 (+.f64 (+.f64 e d) c) b)

series21.0ms (0.3%)

Counts

3 → 144

Calls

3 calls:

8.0ms	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
8.0ms	(+.f64 (+.f64 (+.f64 e d) c) b)
4.0ms	(+.f64 (+.f64 e d) c)

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
31×	`add-log-exp_binary64`
29×	`distribute-lft-out_binary64`
19×	`sum-log_binary64`
15×	`fma-def_binary64`

Counts

3 → 72

Calls

3 calls:

9.0ms	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
7.0ms	(+.f64 (+.f64 (+.f64 e d) c) b)
6.0ms	(+.f64 (+.f64 e d) c)

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

599×	`associate-+l+_binary64`
542×	`fma-neg_binary64`
494×	`associate--l+_binary64`
363×	`associate-+r+_binary64`
350×	`fma-def_binary64`

Counts

216 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	2097
1	284	2070
2	933	2052
3	2956	2052
4	4610	2052
5	4829	2052

prune85.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	3	112

Error

Counts

112 → 3

Alt Table

Status	Error	Program
	0.5b	(+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c) b) a)
▶	0.0b	(log.f64 (.f64 (.f64 (.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b)) (exp.f64 a)))
	0.2b	(+.f64 (log.f64 (.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b))) a)

Compiler

Compiled 1704 to 454 computations (73.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series116.0ms (1.8%)

Counts

4 → 168

Calls

4 calls:

58.0ms	(.f64 (.f64 (.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b)) (exp.f64 a))
33.0ms	(.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b))
17.0ms	(.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c))
7.0ms	(*.f64 (exp.f64 e) (exp.f64 d))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64`
34×	`pow1_binary64`
23×	`*-un-lft-identity_binary64`
20×	`cbrt-unprod_binary64`
20×	`prod-exp_binary64`

Counts

4 → 93

Calls

4 calls:

13.0ms	(.f64 (.f64 (.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b)) (exp.f64 a))
11.0ms	(.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b))
7.0ms	(.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c))
5.0ms	(*.f64 (exp.f64 e) (exp.f64 d))

simplify165.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

968×	`prod-exp_binary64`
493×	`*-commutative_binary64`
466×	`fma-def_binary64`
440×	`associate-+l+_binary64`
291×	`associate-+r+_binary64`

Counts

261 → 244

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	347	5120
1	1082	4130
2	2280	3920
3	3203	3914
4	4314	3914
5	5695	3914

prune128.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	244	3	247

Error

Counts

247 → 3

Alt Table

Status	Error	Program
▶	0.1b	(log.f64 (.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 (+.f64 d c))) (exp.f64 b)) (exp.f64 a)))
	0.5b	(+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c) b) a)
✓	0.0b	(log.f64 (.f64 (.f64 (.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b)) (exp.f64 a)))

Compiler

Compiled 5764 to 1663 computations (71.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (exp.f64 e) (exp.f64 (+.f64 d c)))
✓	0.4b	(.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 (+.f64 d c))) (exp.f64 b)) (exp.f64 a))
✓	0.4b	(.f64 (.f64 (exp.f64 e) (exp.f64 (+.f64 d c))) (exp.f64 b))
✓	1.9b	(exp.f64 (+.f64 d c))

series92.0ms (1.4%)

Counts

4 → 168

Calls

4 calls:

46.0ms	(.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 (+.f64 d c))) (exp.f64 b)) (exp.f64 a))
28.0ms	(.f64 (.f64 (exp.f64 e) (exp.f64 (+.f64 d c))) (exp.f64 b))
13.0ms	(*.f64 (exp.f64 e) (exp.f64 (+.f64 d c)))
4.0ms	(exp.f64 (+.f64 d c))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
22×	`exp-prod_binary64`
20×	`add-cbrt-cube_binary64`
20×	`pow1_binary64`
12×	`pow-prod-up_binary64`

Counts

4 → 86

Calls

4 calls:

13.0ms	(.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 (+.f64 d c))) (exp.f64 b)) (exp.f64 a))
9.0ms	(.f64 (.f64 (exp.f64 e) (exp.f64 (+.f64 d c))) (exp.f64 b))
7.0ms	(*.f64 (exp.f64 e) (exp.f64 (+.f64 d c)))
3.0ms	(exp.f64 (+.f64 d c))

simplify480.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

727×	`associate-r_binary64`
727×	`distribute-rgt-out_binary64`
571×	`associate-l_binary64`
402×	`fma-def_binary64`
334×	`prod-exp_binary64`

Counts

254 → 234

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	4635
1	925	3810
2	3583	3654
3	5388	3654

prune158.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	234	3	237

Error

Counts

237 → 3

Alt Table

Status	Error	Program
✓	0.1b	(log.f64 (.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 (+.f64 d c))) (exp.f64 b)) (exp.f64 a)))
▶	0.5b	(+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c) b) a)
✓	0.0b	(log.f64 (.f64 (.f64 (.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b)) (exp.f64 a)))

Compiler

Compiled 5282 to 1539 computations (70.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (+.f64 e d))
✓	0.2b	(+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c) b) a)
✓	0.3b	(+.f64 (fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c) b)
✓	0.4b	(fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c)

series380.0ms (5.9%)

Counts

4 → 104

Calls

4 calls:

129.0ms	(+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c) b) a)
122.0ms	(+.f64 (fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c) b)
109.0ms	(fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c)
19.0ms	(sqrt.f64 (+.f64 e d))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
11×	`add-log-exp_binary64`
10×	`add-sqr-sqrt_binary64`
7×	`fma-def_binary64`
7×	`add-cube-cbrt_binary64`

Counts

4 → 68

Calls

4 calls:

6.0ms	(+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c) b) a)
3.0ms	(sqrt.f64 (+.f64 e d))
2.0ms	(+.f64 (fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c) b)
0.0ms	(fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c)

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

759×	`distribute-rgt-in_binary64`
733×	`distribute-lft-in_binary64`
424×	`fma-def_binary64`
353×	`fma-neg_binary64`
188×	`associate-r_binary64`

Counts

172 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	1937
1	384	1895
2	1033	1870
3	4846	1869
4	5143	1869

prune102.0ms (1.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	179	3	182

Error

Counts

182 → 3

Alt Table

Status	Error	Program
✓	0.1b	(log.f64 (.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 (+.f64 d c))) (exp.f64 b)) (exp.f64 a)))
✓	0.5b	(+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 e d)) (sqrt.f64 (+.f64 e d)) c) b) a)
✓	0.0b	(log.f64 (.f64 (.f64 (.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b)) (exp.f64 a)))

Compiler

Compiled 3686 to 1098 computations (70.2% saved)

regimes1.1s (17.2%)

Accuracy

Total 0.0b remaining (64.8%)

Threshold costs 0.0b (64.8%)

Counts

115 → 1

Compiler

Compiled 20666 to 13493 computations (34.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	20	25
2	20	25

end82.0ms (1.3%)

Remove: (sort a b c d e)
Compiler: Compiled 138 to 99 computations (28.3% saved)

Details

analyze1.9s (29.9%)

sample1.3s (19.5%)

simplify8.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series21.0ms (0.3%)

rewrite26.0ms (0.4%)

simplify89.0ms (1.4%)

prune85.0ms (1.3%)

localize16.0ms (0.2%)

series116.0ms (1.8%)

rewrite44.0ms (0.7%)

simplify165.0ms (2.6%)

prune128.0ms (2%)

localize14.0ms (0.2%)

series92.0ms (1.4%)

rewrite41.0ms (0.6%)

simplify480.0ms (7.4%)

prune158.0ms (2.4%)

localize8.0ms (0.1%)

series380.0ms (5.9%)

rewrite14.0ms (0.2%)

simplify79.0ms (1.2%)

prune102.0ms (1.6%)

regimes1.1s (17.2%)

simplify2.0ms (0%)

end82.0ms (1.3%)

Profiling