Details

sample380.0ms

Algorithm

intervals

Results

174.0ms	69×	body	10240	exit
139.0ms	75×	body	1280	valid
36.0ms	50×	body	640	valid
9.0ms	99×	body	80	valid
6.0ms	20×	body	320	valid
2.0ms	12×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

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)))
0.1b	(sin (expm1 a))
36.2b	(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:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series145.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
80.0ms	(expm1 (sin (expm1 a)))
61.0ms	(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

prune201.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 30.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
36.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

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

series482.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (expm1 (sin (expm1 a))))
159.0ms	(cbrt (expm1 (sin (expm1 a))))
158.0ms	(cbrt (expm1 (sin (expm1 a))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify71.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (66.0ms)

Iter	Nodes	Cost
0	88	549
1	181	487
2	472	481
3	1562	470
4	5001	467

prune309.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
0.6b	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
36.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
19×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
6×	`pow1` `add-exp-log` `unswap-sqr`
4×	`expm1-log1p-u` `pow1/3` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down`
1×	`pow3` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 70

Calls

4 calls:

5.0ms	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
16.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series500.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
160.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
162.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
4.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify83.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	249	1381
1	723	1230
2	2676	1203
3	5001	1111

prune477.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 30.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
2.4b	(exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))
36.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

5.0ms	(log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
10.0ms	(exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series563.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
163.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
178.0ms	(exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))
4.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify129.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 4 (121.0ms)

Iter	Nodes	Cost
0	210	1113
1	446	962
2	1138	938
3	3969	931
4	5001	930

prune363.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 29.6b

regimes506.0ms

Accuracy

0% (2.2b remaining)

Error of 33.3b against oracle of 31.0b and baseline of 33.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	32
1	25	32
2	25	32

end0.0ms

sample12.6s

Algorithm

intervals

Results

6.7s	2693×	body	10240	exit
3.8s	2262×	body	1280	valid
1.1s	1664×	body	640	valid
274.0ms	2844×	body	80	valid
270.0ms	801×	body	320	valid
85.0ms	417×	body	160	valid
32.0ms	7×	body	5120	valid
9.0ms	5×	body	2560	valid