Details

sample361.0ms

Algorithm

intervals

Results

165.0ms	89×	body	1280	valid
63.0ms	62×	body	640	valid
14.0ms	73×	body	80	valid
13.0ms	21×	body	320	valid
5.0ms	11×	body	160	valid

simplify55.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

54.0ms

(/ (* r (sin b)) (cos (+ a b)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize18.0ms

Local error

Found 3 expressions with local error:

3.6b	(cos (+ a b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite71.0ms

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	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))
17.0ms	(* r (sin b))

series258.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

163.0ms	(/ (* r (sin b)) (cos (+ a b)))
69.0ms	(* r (sin b))
26.0ms	(cos (+ a b))

simplify1.5s

Counts

33 → 65

Calls

33 calls:

Slowest

311.0ms	(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
247.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
202.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
198.0ms	(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
192.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune705.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

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)))

rewrite86.0ms

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	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms	(* (sin a) (sin b))
18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* r (sin b))

series542.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

285.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
126.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
66.0ms	(* (sin a) (sin b))
64.0ms	(* r (sin b))

simplify4.1s

Counts

56 → 102

Calls

56 calls:

Slowest

505.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
342.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
333.0ms	(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
311.0ms	(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
305.0ms	(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

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))

rewrite41.0ms

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

16.0ms	(* (sin a) (sin b))
16.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
9.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

308.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
151.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
70.0ms	(* r (sin b))
68.0ms	(* (sin a) (sin b))

simplify2.9s

Counts

46 → 90

Calls

46 calls:

Slowest

441.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
353.0ms	(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
324.0ms	(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
316.0ms	(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
275.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b	(expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
0.2b	(log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
0.2b	(/ (* r (sin b)) (log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b)))))))
0.2b	(* (sin a) (sin b))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

Slowest

12.0ms	(* (sin a) (sin b))
12.0ms	(/ (* r (sin b)) (log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b)))))))
1.0ms	(expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
0.0ms	(log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b))))))

series747.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

345.0ms	(/ (* r (sin b)) (log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b)))))))
174.0ms	(expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
155.0ms	(log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
72.0ms	(* (sin a) (sin b))

simplify3.1s

Counts

38 → 82

Calls

38 calls:

Slowest

386.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b)))))) (log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b))))))) (log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b))))))))
363.0ms	(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
323.0ms	(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b)))))) (log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b))))))) (log1p (expm1 (fma (cos a) (cos b) (- (* (sin a) (sin b))))))))
230.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
217.0ms	(- (exp (- (* (cos a) (cos b)) (* (sin b) (sin a)))) 1)

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes265.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.9s	2974×	body	1280	valid
2.0s	1769×	body	640	valid
481.0ms	2126×	body	80	valid
464.0ms	764×	body	320	valid
132.0ms	368×	body	160	valid