Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 53 to 38 computations (28.3% saved)

sample1.3s (32.6%)

Infinites

0% of outputs are infinite.

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 (0.2%)

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

prune1.0ms (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)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series20.0ms (0.5%)

Counts

3 → 144

Calls

3 calls:

10.0ms	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
6.0ms	(+.f64 (+.f64 (+.f64 e d) c) b)
4.0ms	(+.f64 (+.f64 e d) c)

rewrite26.0ms (0.7%)

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:

10.0ms	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
6.0ms	(+.f64 (+.f64 (+.f64 e d) c) b)
4.0ms	(+.f64 (+.f64 e d) c)

simplify86.0ms (2.1%)

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 → 107

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

prune67.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	4	108

Error

Counts

108 → 4

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) a)
✓	0.4b	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
	0.3b	(+.f64 (log1p.f64 (expm1.f64 (+.f64 c (+.f64 d (+.f64 b e))))) 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 1682 to 447 computations (73.4% saved)

localize14.0ms (0.3%)

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))

series121.0ms (3%)

Counts

4 → 168

Calls

4 calls:

62.0ms	(.f64 (.f64 (.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b)) (exp.f64 a))
38.0ms	(.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b))
15.0ms	(.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c))
6.0ms	(*.f64 (exp.f64 e) (exp.f64 d))

rewrite40.0ms (1%)

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:

12.0ms	(.f64 (.f64 (.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b)) (exp.f64 a))
12.0ms	(.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c)) (exp.f64 b))
6.0ms	(.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 c))
5.0ms	(*.f64 (exp.f64 e) (exp.f64 d))

simplify157.0ms (3.9%)

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

prune141.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	244	4	248

Error

Counts

248 → 4

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) a)
✓	0.4b	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
▶	0.1b	(log.f64 (.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 (+.f64 b c))) (exp.f64 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 5786 to 1672 computations (71.1% saved)

localize13.0ms (0.3%)

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 (+.f64 b c)))
✓	0.4b	(.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 (+.f64 b c))) (exp.f64 a))
✓	1.4b	(exp.f64 (+.f64 b c))

series75.0ms (1.9%)

Counts

3 → 132

Calls

3 calls:

45.0ms	(.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 (+.f64 b c))) (exp.f64 a))
26.0ms	(.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 (+.f64 b c)))
4.0ms	(exp.f64 (+.f64 b c))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
18×	`exp-prod_binary64`
17×	`add-cbrt-cube_binary64`
17×	`pow1_binary64`
10×	`pow-prod-up_binary64`

Counts

3 → 64

Calls

3 calls:

11.0ms	(.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 (+.f64 b c))) (exp.f64 a))
8.0ms	(.f64 (.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 (+.f64 b c)))
3.0ms	(exp.f64 (+.f64 b c))

simplify87.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-r_binary64`
569×	`distribute-rgt-out_binary64`
543×	`associate-l_binary64`
364×	`prod-exp_binary64`
307×	`fma-def_binary64`

Counts

196 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	3860
1	802	3098
2	3005	2912
3	4987	2912

prune132.0ms (3.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	223	4	227

Error

Counts

227 → 4

Alt Table

Status	Error	Program
▶	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) a)
✓	0.4b	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
✓	0.1b	(log.f64 (.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 (+.f64 b c))) (exp.f64 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 4954 to 1405 computations (71.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b))
	0.2b	(+.f64 (+.f64 e d) c)
	0.2b	(+.f64 (+.f64 (+.f64 e d) c) b)
✓	0.4b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) a)

series684.0ms (17.1%)

Counts

2 → 44

Calls

2 calls:

583.0ms	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) a)
101.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
6×	`distribute-lft-out_binary64`
6×	`sqrt-prod_binary64`
6×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 31

Calls

2 calls:

8.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b))
0.0ms	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) a)

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

584×	`distribute-rgt-in_binary64`
576×	`distribute-lft-in_binary64`
526×	`fma-neg_binary64`
500×	`fma-def_binary64`
304×	`associate-r_binary64`

Counts

75 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	1539
1	401	1489
2	1193	1465
3	4840	1465
4	5305	1465

prune136.0ms (3.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	267	4	271

Error

Counts

271 → 4

Alt Table

Status	Error	Program
✓	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) a)
✓	0.4b	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
✓	0.1b	(log.f64 (.f64 (.f64 (*.f64 (exp.f64 e) (exp.f64 d)) (exp.f64 (+.f64 b c))) (exp.f64 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 7380 to 1564 computations (78.8% saved)

regimes687.0ms (17.2%)

Accuracy

Total 0.0b remaining (81.9%)

Threshold costs 0.0b (81.9%)

Counts

75 → 1

Compiler

Compiled 13251 to 9136 computations (31.1% saved)

simplify2.0ms (0.1%)

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 (2.1%)

Remove: (sort a b c d e)
Compiler: Compiled 156 to 108 computations (30.8% saved)

Details

analyze3.0ms (0.1%)

sample1.3s (32.6%)

simplify8.0ms (0.2%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series20.0ms (0.5%)

rewrite26.0ms (0.7%)

simplify86.0ms (2.1%)

prune67.0ms (1.7%)

localize14.0ms (0.3%)

series121.0ms (3%)

rewrite40.0ms (1%)

simplify157.0ms (3.9%)

prune141.0ms (3.5%)

localize13.0ms (0.3%)

series75.0ms (1.9%)

rewrite26.0ms (0.7%)

simplify87.0ms (2.2%)

prune132.0ms (3.3%)

localize8.0ms (0.2%)

series684.0ms (17.1%)

rewrite10.0ms (0.2%)

simplify63.0ms (1.6%)

prune136.0ms (3.4%)

regimes687.0ms (17.2%)

simplify2.0ms (0.1%)

end82.0ms (2.1%)

Profiling