Details

sample358.0ms

Algorithm

intervals

Results

115.0ms	102×	body	1280	valid
81.0ms	62×	body	640	valid
19.0ms	35×	body	320	valid
12.0ms	51×	body	80	valid
2.0ms	6×	body	160	valid

simplify33.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize20.0ms

Local error

Found 3 expressions with local error:

5.7b	(cos (+ a b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite63.0ms

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

26.0ms	(cos (+ a b))
17.0ms	(* r (sin b))
17.0ms	(/ (* r (sin b)) (cos (+ a b)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

152.0ms	(/ (* r (sin b)) (cos (+ a b)))
73.0ms	(* r (sin b))
26.0ms	(cos (+ a b))

simplify1.0s

Counts: 65 → 65

prune749.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

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

37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
35.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms	(* r (sin b))
11.0ms	(* (sin a) (sin b))

series603.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

352.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
127.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms	(* (sin a) (sin b))
57.0ms	(* r (sin b))

simplify1.9s

Counts: 102 → 102

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

55.3b	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))
0.3b	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

Slowest

21.0ms	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
14.0ms	(* (sin b) (sin a))
11.0ms	(* (sin b) (sin a))
0.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

512.0ms	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
74.0ms	(* (sin b) (sin a))
69.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))
69.0ms	(* (sin b) (sin a))

simplify2.0s

Counts: 95 → 95

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

55.2b	(fma (- (sin b)) (sin a) (log1p (expm1 (* (sin b) (sin a)))))
0.3b	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (log1p (expm1 (* (sin b) (sin a)))))))
0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

Slowest

19.0ms	(* (sin b) (sin a))
15.0ms	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (log1p (expm1 (* (sin b) (sin a)))))))
12.0ms	(* (sin b) (sin a))
0.0ms	(fma (- (sin b)) (sin a) (log1p (expm1 (* (sin b) (sin a)))))

series791.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

565.0ms	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (log1p (expm1 (* (sin b) (sin a)))))))
106.0ms	(fma (- (sin b)) (sin a) (log1p (expm1 (* (sin b) (sin a)))))
61.0ms	(* (sin b) (sin a))
59.0ms	(* (sin b) (sin a))

simplify2.2s

Counts: 95 → 95

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes320.0ms

Accuracy

0% (0.3b remaining)

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

bsearch9.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.4s	2921×	body	1280	valid
2.0s	1789×	body	640	valid
448.0ms	2168×	body	80	valid
445.0ms	759×	body	320	valid
175.0ms	367×	body	160	valid