Details

sample337.0ms

Algorithm

intervals

Results

160.0ms	65×	body	10240	exit
111.0ms	65×	body	1280	valid
30.0ms	46×	body	640	valid
14.0ms	106×	body	80	valid
8.0ms	24×	body	320	valid
3.0ms	15×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
34.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(expm1 (sin (expm1 a)))
1.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series152.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
84.0ms	(expm1 (sin (expm1 a)))
63.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify121.0ms

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

prune207.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 28.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
34.1b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod`
1×	`rem-log-exp` `sin-diff` `rem-exp-log` `expm1-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(sin (expm1 a))
1.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
1.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series94.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sin (expm1 a))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
33.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify79.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	108	467
1	208	407
2	487	407
3	1838	407
4	5001	407

prune256.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 28.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
34.2b	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod` `*-un-lft-identity`
6×	`pow1` `log-prod` `log-pow` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`rem-exp-log`
1×	`pow1/2` `rem-log-exp`

Counts

4 → 57

Calls

4 calls:

4.0ms	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
1.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series170.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
28.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
29.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify100.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 7 (93.0ms)

Iter	Nodes	Cost
0	76	773
1	100	678
2	127	678
3	187	678
4	358	678
5	884	678
6	3890	678
7	5001	666

prune369.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 28.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
34.1b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
34.1b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
34.1b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod`
1×	`rem-exp-log`

Counts

4 → 40

Calls

4 calls:

1.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series39.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify76.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	498
1	64	429
2	83	429
3	124	429
4	224	429
5	546	429
6	2617	429
7	5001	429

prune244.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 28.4b

regimes332.0ms

Accuracy

0% (1.7b remaining)

Error of 33.0b against oracle of 31.2b and baseline of 33.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	45
1	21	45

end0.0ms

sample12.2s

Algorithm

intervals

Results

6.5s	2598×	body	10240	exit
3.7s	2217×	body	1280	valid
1.1s	1609×	body	640	valid
291.0ms	2887×	body	80	valid
280.0ms	855×	body	320	valid
87.0ms	422×	body	160	valid
18.0ms	4×	body	5120	valid
11.0ms	6×	body	2560	valid