Details

sample76.0ms

Algorithm

intervals

Results

42.0ms	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

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

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

series155.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* r (sin b))
96.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify33.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	207	327
1	884	279
2	5001	279

prune157.0ms

Filtered

62 candidates to 46 candidates (74.2%)

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

7.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
3.0ms	(* r (sin b))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
36.0ms	(* r (sin b))
45.0ms	(* (sin a) (sin b))
209.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	369	835
1	1591	735
2	5002	730

prune326.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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 b) (cos a)) (* (sin a) (sin b)))
25.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
212.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
45.0ms	(* (sin a) (sin b))
110.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	427	1385
1	1819	1256
2	5001	1254

prune406.0ms

Filtered

122 candidates to 94 candidates (77.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

26.0ms	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
4.0ms	(* (sin a) (sin b))
10.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
28.0ms	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
45.0ms	(* (sin a) (sin b))
95.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
111.0ms	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	473	1553
1	2023	1336
2	5002	1307

prune362.0ms

Filtered

138 candidates to 89 candidates (64.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes134.0ms

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	20	11
1	20	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2950×	body	1280	valid
452.0ms	1794×	body	640	valid
138.0ms	756×	body	320	valid
116.0ms	2132×	body	80	valid
45.0ms	370×	body	160	valid