Details

sample425.0ms

Algorithm

intervals

Results

200.0ms	71×	body	5120	exit
150.0ms	88×	body	1280	valid
39.0ms	53×	body	640	valid
9.0ms	82×	body	80	valid
8.0ms	22×	body	320	valid
5.0ms	1×	body	5120	valid
2.0ms	10×	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: 35.4b

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))
40.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite8.0ms

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)))
3.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series164.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
85.0ms	(expm1 (sin (expm1 a)))
69.0ms	(sin (expm1 a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify129.0ms

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

prune198.0ms

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: 34.2b

Counts

52 → 13

localize15.0ms

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)
40.6b	(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)

series97.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(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)

simplify150.0ms

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

prune265.0ms

Filtered

79 candidates to 46 candidates (58.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	72	20	92

Merged error: 33.8b

Counts

92 → 20

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.6b	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
40.5b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite14.0ms

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:

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

series190.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
2.0ms	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
37.0ms	(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)

simplify48.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (32.0ms)

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

prune434.0ms

Filtered

111 candidates to 67 candidates (60.4%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	3	16	19
Picked	1	0	1
Done	0	0	0
Total	104	27	131

Merged error: 33.5b

Counts

131 → 27

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.7b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
1.0b	(pow (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)
40.6b	(fmod (cbrt (pow (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite14.0ms

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`
2×	`cbrt-prod` `pow1/3`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 56

Calls

4 calls:

5.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
5.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
2.0ms	(pow (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series333.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
145.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
36.0ms	(pow (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)
4.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify145.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	167	1914
1	519	1602
2	3301	1594
3	5001	1594

prune264.0ms

Filtered

68 candidates to 49 candidates (72.1%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	2	24	26
Picked	0	1	1
Done	0	0	0
Total	63	32	95

Merged error: 33.3b

Counts

95 → 32

regimes394.0ms

Accuracy

0% (2.0b remaining)

Error of 33.5b against oracle of 31.4b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	21	39

end0.0ms

sample13.2s

Algorithm

intervals

Results

7.2s	2639×	body	5120	exit
3.9s	2311×	body	1280	valid
1.2s	1679×	body	640	valid
315.0ms	2816×	body	80	valid
288.0ms	802×	body	320	valid
88.0ms	383×	body	160	valid
19.0ms	4×	body	5120	valid
10.0ms	5×	body	2560	valid