Details

sample364.0ms

Algorithm

intervals

Results

194.0ms	72×	body	10240	exit
99.0ms	69×	body	1280	valid
41.0ms	63×	body	640	valid
9.0ms	85×	body	80	valid
7.0ms	23×	body	320	valid
4.0ms	16×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Merged error: 34.3b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
39.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

Calls

4 calls:

1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series154.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
87.0ms	(expm1 (sin (expm1 a)))
63.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify123.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	108	302
1	242	264
2	720	264
3	2933	264
4	5001	264

prune197.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	38	13	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	13	52

Merged error: 32.9b

Counts

52 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
0.6b	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.3b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `sin-diff` `rem-cbrt-cube` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 67

Calls

4 calls:

2.0ms	(sin (expm1 a))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
2.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series100.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sin (expm1 a))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
33.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify145.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	156	650
1	538	592
2	3301	586
3	5002	586

prune266.0ms

Filtered

79 candidates to 45 candidates (57.0%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	73	19	92

Merged error: 32.7b

Counts

92 → 19

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0b	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
39.3b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
26×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
7×	`add-exp-log` `pow1/3`
6×	`unpow-prod-down` `cube-prod` `swap-sqr` `associate-r` `associate-l`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `pow-prod-down` `pow-sqr` `pow-prod-up` `sqr-pow`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 99

Calls

4 calls:

2.0ms	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
7.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
2.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series188.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
149.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
34.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify44.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	235	1703
1	842	1547
2	5001	1346

prune430.0ms

Filtered

111 candidates to 67 candidates (60.4%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	2	16	18
Picked	0	1	1
Done	0	0	0
Total	104	26	130

Merged error: 32.4b

Counts

130 → 26

localize31.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
39.3b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
39.3b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
39.3b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 52

Calls

4 calls:

2.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series43.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify131.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	104	1238
1	355	1048
2	2725	916
3	5002	881

prune301.0ms

Filtered

64 candidates to 47 candidates (73.4%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	1	23	24
Picked	1	0	1
Done	0	1	1
Total	61	29	90

Merged error: 32.3b

Counts

90 → 29

regimes381.0ms

Accuracy

0% (2.0b remaining)

Error of 34.0b against oracle of 32.0b and baseline of 34.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	68
1	27	68

end0.0ms

sample13.0s

Algorithm

intervals

Results

7.1s	2622×	body	10240	exit
3.9s	2345×	body	1280	valid
1.1s	1653×	body	640	valid
286.0ms	2737×	body	80	valid
280.0ms	830×	body	320	valid
92.0ms	427×	body	160	valid
23.0ms	5×	body	5120	valid
6.0ms	3×	body	2560	valid