Details

sample690.0ms

Algorithm

intervals

Results

179.0ms	92×	body	1280	valid
164.0ms	53×	body	640	valid
84.0ms	26×	body	320	valid
15.0ms	74×	body	80	valid
6.0ms	11×	body	160	valid

simplify49.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize21.0ms

Local error

Found 3 expressions with local error:

3.5b	(cos (+ a b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite660.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 56

Calls

3 calls:

Slowest

610.0ms	(cos (+ a b))
27.0ms	(/ (* r (sin b)) (cos (+ a b)))
19.0ms	(* r (sin b))

series429.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

310.0ms	(/ (* r (sin b)) (cos (+ a b)))
68.0ms	(* r (sin b))
51.0ms	(cos (+ a b))

simplify784.0ms

Counts: 65 → 65

prune684.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l*`

Counts

4 → 90

Calls

4 calls:

Slowest

39.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
35.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
22.0ms	(* (sin a) (sin b))
19.0ms	(* r (sin b))

series606.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

322.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
130.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
85.0ms	(* (sin a) (sin b))
69.0ms	(* r (sin b))

simplify1.9s

Counts: 102 → 102

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 78

Calls

4 calls:

Slowest

23.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
15.0ms	(* (sin a) (sin b))
8.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

336.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
134.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
62.0ms	(* (sin a) (sin b))
50.0ms	(* r (sin b))

simplify1.5s

Counts: 90 → 90

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 78

Calls

4 calls:

Slowest

26.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
11.0ms	(* (sin a) (sin b))
9.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

405.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
164.0ms	(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
70.0ms	(* (sin a) (sin b))
67.0ms	(* r (sin b))

simplify1.3s

Counts: 90 → 90

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes250.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.7s	2981×	body	1280	valid
1.4s	1785×	body	640	valid
438.0ms	779×	body	320	valid
338.0ms	2101×	body	80	valid
128.0ms	357×	body	160	valid