Details

sample297.0ms

Algorithm

intervals

Results

92.0ms	94×	body	1280	valid
46.0ms	63×	body	80	valid
41.0ms	59×	body	640	valid
14.0ms	26×	body	320	valid
5.0ms	14×	body	160	valid

simplify44.0ms

Calls

1 calls:

Slowest

44.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize32.0ms

Local error

Found 3 expressions with local error:

2.9b	(cos (+ a b))
0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l` `add-log-exp`
2×	`div-inv`
1×	`cbrt-undiv` `cos-sum` `clear-num` `frac-2neg` `div-exp` `associate-r/` `-commutative`

Calls

3 calls:

Slowest

14.0ms	(/ (sin b) (cos (+ a b)))
3.0ms	(cos (+ a b))
3.0ms	(* r (/ (sin b) (cos (+ a b))))

series138.0ms

Calls

3 calls:

Slowest

83.0ms	(* r (/ (sin b) (cos (+ a b))))
34.0ms	(/ (sin b) (cos (+ a b)))
20.0ms	(cos (+ a b))

simplify1.3s

Calls

49 calls:

Slowest

279.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
196.0ms	(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
163.0ms	(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
159.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
45.0ms	(/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))

prune752.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
18×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
7×	`sin-mult`
6×	`pow1` `cos-mult` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `flip3--` `associate-l` `frac-sub` `flip--` `associate-/l` `sub-div`
2×	`*-commutative` `div-inv`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`

Calls

4 calls:

Slowest

17.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))

series541.0ms

Calls

4 calls:

Slowest

225.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
150.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
93.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
73.0ms	(* (sin a) (sin b))

simplify4.0s

Calls

70 calls:

Slowest

341.0ms	(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
333.0ms	(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
318.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
271.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
226.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

26.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
3.0ms	(* r (sin b))

series518.0ms

Calls

4 calls:

Slowest

295.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
115.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
72.0ms	(* (sin a) (sin b))
35.0ms	(* r (sin b))

simplify2.6s

Calls

42 calls:

Slowest

346.0ms	(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
297.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
296.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
251.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
242.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

16.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
16.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
9.0ms	(* (sin b) (sin a))
3.0ms	(* r (sin b))

series482.0ms

Calls

4 calls:

Slowest

285.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
97.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
51.0ms	(* (sin b) (sin a))
48.0ms	(* r (sin b))

simplify2.3s

Calls

42 calls:

Slowest

384.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- b a)) (cos (+ b a)))))
259.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos a) (cos b)) (* (sin b) (sin a)))))
231.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
210.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (- (* (cos a) (cos b)) (* (sin b) (sin a))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
163.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes295.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.8s	2903×	body	1280	valid
1.9s	1812×	body	640	valid
603.0ms	835×	body	320	valid
418.0ms	2100×	body	80	valid
154.0ms	350×	body	160	valid