Details

sample75.0ms

Algorithm

intervals

Results

39.0ms	88×	body	1280	valid
14.0ms	57×	body	640	valid
5.0ms	71×	body	80	valid
5.0ms	28×	body	320	valid
1.0ms	12×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.0b	(cos (+ a b))

rewrite15.0ms

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:

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

series153.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* r (sin b))
94.0ms	(/ (* 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

prune155.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(- (* (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))))

rewrite26.0ms

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×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `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 → 87

Calls

4 calls:

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

series367.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos a) (cos b))
79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* (sin a) (sin b))
205.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify48.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	397	865
1	1625	767
2	5001	757

prune316.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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))
0.3b	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

rewrite47.0ms

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)))
24.0ms	(* 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))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
210.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
42.0ms	(* (sin a) (sin b))
106.0ms	(/ (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	1384
1	1819	1255
2	5001	1254

prune398.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

0.0ms	(log1p (* (sin a) (sin b)))
4.0ms	(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(log1p (* (sin a) (sin b)))
112.0ms	(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
47.0ms	(* (sin a) (sin b))
258.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	389	982
1	1599	774
2	5001	767

prune277.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes142.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	2952×	body	1280	valid
441.0ms	1752×	body	640	valid
141.0ms	811×	body	320	valid
120.0ms	2134×	body	80	valid
49.0ms	351×	body	160	valid