Details

sample79.0ms

Algorithm

intervals

Results

45.0ms	108×	body	1280	valid
14.0ms	55×	body	640	valid
5.0ms	30×	body	320	valid
4.0ms	52×	body	80	valid
1.0ms	11×	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: 15.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.0b	(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×	`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))

series159.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* r (sin b))
97.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify36.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (7.0ms)

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

prune161.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin 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))))

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×	`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:

3.0ms	(* r (sin b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* r (sin b))
83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
215.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (40.0ms)

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

prune334.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
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)))))

rewrite13.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

3.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))
4.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* r (sin b))
82.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
43.0ms	(* (sin a) (sin b))
221.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	273	680
1	1161	578
2	5002	578

prune298.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

3.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (log1p (expm1 (* (sin a) (sin b))))))
4.0ms	(* (sin a) (sin b))
4.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (log1p (expm1 (* (sin a) (sin b)))))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* r (sin b))
119.0ms	(fma (cos a) (cos b) (- (log1p (expm1 (* (sin a) (sin b))))))
44.0ms	(* (sin a) (sin b))
263.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (log1p (expm1 (* (sin a) (sin b)))))))

simplify36.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	272	768
1	1162	631
2	5001	625

prune281.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes166.0ms

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	16	12
1	16	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2923×	body	1280	valid
464.0ms	1813×	body	640	valid
136.0ms	769×	body	320	valid
118.0ms	2135×	body	80	valid
46.0ms	360×	body	160	valid