Details

sample329.0ms

Algorithm

intervals

Results

40.0ms	90×	body	1280	valid
17.0ms	52×	body	640	valid
5.0ms	80×	body	80	valid
4.0ms	22×	body	320	valid
2.0ms	12×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	5

prune4.0ms

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: 15.3b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.4b	(cos (+ a b))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

7.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series159.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	263	560
1	1093	504
2	5002	504

prune218.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 0.2b

Counts

83 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* (sin a) (sin b))
215.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
114.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	432	1385
1	1847	1256
2	5002	1249

prune401.0ms

Filtered

122 candidates to 96 candidates (78.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	108	14	122
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	118	15	133

Merged error: 0.0b

Counts

133 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
0.2b	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`frac-2neg` `associate-*r/` `clear-num` `fma-udef` `sin-mult`

Counts

4 → 94

Calls

4 calls:

1.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))
7.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
4.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
44.0ms	(* (sin a) (sin b))
217.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
118.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	329	1173
1	1413	1043
2	5001	1043

prune338.0ms

Filtered

106 candidates to 82 candidates (77.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	107	14	121

Merged error: 0.0b

Counts

121 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))))
0.2b	(/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`frac-2neg` `associate-*r/` `clear-num` `fma-udef` `sin-mult`

Counts

4 → 94

Calls

4 calls:

1.0ms	(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
5.0ms	(* (sin a) (sin b))
7.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))))
4.0ms	(/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
45.0ms	(* (sin a) (sin b))
267.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))))
159.0ms	(/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	328	1353
1	1406	1165
2	5002	1160

prune332.0ms

Filtered

106 candidates to 85 candidates (80.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	106	14	120

Merged error: 0.0b

Counts

120 → 14

regimes197.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	12
1	16	12

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2913×	body	1280	valid
482.0ms	1861×	body	640	valid
157.0ms	789×	body	320	valid
124.0ms	2079×	body	80	valid
54.0ms	360×	body	160	valid