Details

sample78.0ms

Algorithm

intervals

Results

43.0ms	101×	body	1280	valid
13.0ms	52×	body	640	valid
6.0ms	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

localize16.0ms

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))

rewrite16.0ms

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×	`times-frac` `associate-r` `associate-l` `associate-/r*` `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 → 47

Calls

3 calls:

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

series158.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* r (sin b))
97.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify34.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune135.0ms

Filtered

56 candidates to 40 candidates (71.4%)

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))))

rewrite24.0ms

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×	`associate-/r/` `cos-mult`
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` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* r (sin b))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* r (sin b))
45.0ms	(* (sin a) (sin b))
220.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune285.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (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`
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` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

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))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
217.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
50.0ms	(* (sin a) (sin b))
114.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	401	1307
1	1733	1182
2	5001	1178

prune380.0ms

Filtered

112 candidates to 84 candidates (75.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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×	`associate-*r/` `cos-mult` `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 → 118

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))))
27.0ms	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
43.0ms	(* (sin a) (sin b))
98.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
118.0ms	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	456	1487
1	1977	1272
2	5002	1240

prune335.0ms

Filtered

130 candidates to 81 candidates (62.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes144.0ms

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

sample2.3s

Algorithm

intervals

Results

1.3s	2950×	body	1280	valid
455.0ms	1794×	body	640	valid
138.0ms	756×	body	320	valid
127.0ms	2132×	body	80	valid
52.0ms	370×	body	160	valid