Details

sample318.0ms

Algorithm

intervals

Results

46.0ms	101×	body	1280	valid
13.0ms	52×	body	640	valid
5.0ms	31×	body	320	valid
3.0ms	57×	body	80	valid
2.0ms	15×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite38.0ms

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:

10.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series160.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify40.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

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

prune222.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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)))
28.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
214.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
44.0ms	(* (sin a) (sin b))
113.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	432	1384
1	1847	1255
2	5001	1249

prune420.0ms

Filtered

122 candidates to 96 candidates (78.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
4.5b	(log (exp (* (sin a) (sin b))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-l`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`log-prod` `prod-exp` `associate-/r` `log-pow` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `div-inv`
1×	`exp-prod` `exp-to-pow` `frac-2neg` `associate-*r/` `rem-log-exp` `clear-num` `sin-mult`

Counts

4 → 104

Calls

4 calls:

26.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
4.0ms	(* (sin a) (sin b))
11.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.0ms	(log (exp (* (sin a) (sin b))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
46.0ms	(* (sin a) (sin b))
110.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
44.0ms	(log (exp (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	375	1363
1	1590	1188
2	5001	1184

prune449.0ms

Filtered

116 candidates to 92 candidates (79.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`expm1-log1p-u` `cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `flip--` `div-inv` `sub-div` `unswap-sqr`
1×	`pow-flip` `frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 122

Calls

4 calls:

4.0ms	(* r (sin b))
5.0ms	(* (sin a) (sin b))
11.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* r (sin b))
43.0ms	(* (sin a) (sin b))
95.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
213.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	490	1317
1	2461	1134
2	5001	1106

prune359.0ms

Filtered

134 candidates to 85 candidates (63.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes176.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	12
1	17	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	2950×	body	1280	valid
465.0ms	1794×	body	640	valid
141.0ms	756×	body	320	valid
117.0ms	2132×	body	80	valid
47.0ms	370×	body	160	valid