Details

sample442.0ms

Algorithm

intervals

Results

239.0ms	87×	body	10240	exit
139.0ms	87×	body	1280	valid
33.0ms	50×	body	640	valid
9.0ms	85×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	9×	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: 34.6b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

2×	`expm1-udef`
1×	`sin-diff`

Counts

4 → 2

Calls

4 calls:

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

series158.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sin (expm1 a))
92.0ms	(expm1 (sin (expm1 a)))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify93.0ms

Algorithm

egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	69	64
1	167	62
2	528	62
3	2131	62
4	5001	62

prune22.0ms

Filtered

14 candidates to 4 candidates (28.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	2	15

Merged error: 34.3b

Counts

15 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cos (exp a)) (sin 1))
0.7b	(* (sin (exp a)) (cos 1))
2.5b	(- (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)))
21.8b	(fmod (atan2 (expm1 (- (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)))) (atan a)) a)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-commutative`
4×	`prod-diff`
2×	`fma-neg`
1×	`sub-neg` `flip3--` `sin-cos-mult` `flip--`

Counts

4 → 13

Calls

4 calls:

3.0ms	(* (cos (exp a)) (sin 1))
7.0ms	(* (sin (exp a)) (cos 1))
8.0ms	(- (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)))
1.0ms	(fmod (atan2 (expm1 (- (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)))) (atan a)) a)

series710.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (cos (exp a)) (sin 1))
141.0ms	(* (sin (exp a)) (cos 1))
407.0ms	(- (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)))
12.0ms	(fmod (atan2 (expm1 (- (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)))) (atan a)) a)

simplify105.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	209	297
1	789	281
2	3340	266
3	5001	254

prune88.0ms

Filtered

25 candidates to 12 candidates (48.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	22	5	27

Merged error: 33.8b

Counts

27 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cos (exp a)) (sin 1))
2.5b	(- (exp a) 1)
40.0b	(fmod (atan2 (expm1 (- (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) (* (cos (exp a)) (sin 1)))) (atan a)) a)
41.0b	(- (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) (* (cos (exp a)) (sin 1)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

3×	`div-inv`
2×	`sub-neg` `flip3--` `prod-diff` `*-commutative` `flip--`
1×	`associate--l-` `associate-+l-` `expm1-def` `fma-neg` `div-sub` `sin-diff`

Counts

4 → 14

Calls

4 calls:

3.0ms	(* (cos (exp a)) (sin 1))
3.0ms	(- (exp a) 1)
1.0ms	(fmod (atan2 (expm1 (- (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) (* (cos (exp a)) (sin 1)))) (atan a)) a)
13.0ms	(- (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) (* (cos (exp a)) (sin 1)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (cos (exp a)) (sin 1))
13.0ms	(- (exp a) 1)
10.0ms	(fmod (atan2 (expm1 (- (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) (* (cos (exp a)) (sin 1)))) (atan a)) a)
333.0ms	(- (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) (* (cos (exp a)) (sin 1)))

simplify113.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	273	332
1	996	315
2	4574	305
3	5001	302

prune128.0ms

Filtered

26 candidates to 16 candidates (61.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	24	7	31

Merged error: 33.8b

Counts

31 → 7

localize39.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (exp a) 1)
2.5b	(- (exp a) 1)
40.0b	(fmod (atan2 (expm1 (/ (- (pow (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) 3) (pow (* (cos (exp a)) (sin 1)) 3)) (fma (fma 1/2 (sin (+ (exp a) 1)) (* 1/2 (sin (- (exp a) 1)))) (fma (cos (exp a)) (sin 1) (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2)) (* (* (cos (exp a)) (cos (exp a))) (pow (sin 1) 2))))) (atan a)) a)
40.9b	(- (pow (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) 3) (pow (* (cos (exp a)) (sin 1)) 3))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`prod-diff`
11×	`unpow-prod-down`
10×	`sqr-pow`
8×	`unpow3`
5×	`div-inv`
3×	`sub-neg` `flip3--` `fma-neg` `*-commutative` `flip--`
2×	`expm1-def`
1×	`difference-cubes` `difference-of-squares`

Counts

4 → 31

Calls

4 calls:

3.0ms	(- (exp a) 1)
3.0ms	(- (exp a) 1)
1.0ms	(fmod (atan2 (expm1 (/ (- (pow (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) 3) (pow (* (cos (exp a)) (sin 1)) 3)) (fma (fma 1/2 (sin (+ (exp a) 1)) (* 1/2 (sin (- (exp a) 1)))) (fma (cos (exp a)) (sin 1) (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2)) (* (* (cos (exp a)) (cos (exp a))) (pow (sin 1) 2))))) (atan a)) a)
15.0ms	(- (pow (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) 3) (pow (* (cos (exp a)) (sin 1)) 3))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (exp a) 1)
13.0ms	(- (exp a) 1)
50.0ms	(fmod (atan2 (expm1 (/ (- (pow (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) 3) (pow (* (cos (exp a)) (sin 1)) 3)) (fma (fma 1/2 (sin (+ (exp a) 1)) (* 1/2 (sin (- (exp a) 1)))) (fma (cos (exp a)) (sin 1) (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2)) (* (* (cos (exp a)) (cos (exp a))) (pow (sin 1) 2))))) (atan a)) a)
1.0s	(- (pow (/ (+ (sin (- (exp a) 1)) (sin (+ (exp a) 1))) 2) 3) (pow (* (cos (exp a)) (sin 1)) 3))

simplify74.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	566	1126
1	2384	895
2	5001	886

prune253.0ms

Filtered

43 candidates to 23 candidates (53.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	1	2	3
Picked	1	0	1
Done	0	3	3
Total	42	8	50

Merged error: 33.8b

Counts

50 → 8

regimes296.0ms

Accuracy

0% (0.7b remaining)

Error of 33.6b against oracle of 32.8b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7

end0.0ms

sample13.2s

Algorithm

intervals

Results

7.3s	2710×	body	10240	exit
3.9s	2336×	body	1280	valid
1.1s	1636×	body	640	valid
286.0ms	2792×	body	80	valid
264.0ms	783×	body	320	valid
95.0ms	444×	body	160	valid
27.0ms	5×	body	5120	valid
8.0ms	4×	body	2560	valid