Details

Time bar (total: 53.6s)

sample310.0ms

Algorithm
intervals
Results
104.0ms62×body640valid
100.0ms79×body1280valid
18.0ms79×body80valid
14.0ms25×body320valid
4.0ms11×body160valid

simplify64.0ms

Calls
1 calls:
Slowest
64.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize35.0ms

Local error

Found 3 expressions with local error:

3.0b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite60.0ms

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×associate-/r* times-frac associate-*r* associate-*l* insert-posit16 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
Calls
3 calls:
Slowest
24.0ms
(/ (* r (sin b)) (cos (+ a b)))
18.0ms
(cos (+ a b))
16.0ms
(* r (sin b))

series255.0ms

Calls
3 calls:
Slowest
133.0ms
(/ (* r (sin b)) (cos (+ a b)))
70.0ms
(* r (sin b))
52.0ms
(cos (+ a b))

simplify1.3s

Calls
33 calls:
Slowest
273.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
190.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
173.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
170.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
161.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune660.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

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)))

rewrite76.0ms

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×associate-/r/ cos-mult insert-posit16
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 diff-log div-inv associate-/l*
Calls
4 calls:
Slowest
32.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series571.0ms

Calls
4 calls:
Slowest
344.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
116.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
57.0ms
(* r (sin b))
55.0ms
(* (sin a) (sin b))

simplify3.6s

Calls
53 calls:
Slowest
342.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
332.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
305.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
302.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
300.0ms
(/ (* (* (* r r) r) (* (* (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)))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×associate-*r*
19×times-frac
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
4×insert-posit16
3×associate-/r* flip3-- prod-exp frac-sub cbrt-unprod flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num sub-neg frac-2neg diff-log associate-*r/
Calls
4 calls:
Slowest
98.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
23.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms
(* (sin a) (sin b))

series554.0ms

Calls
4 calls:
Slowest
290.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
119.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
96.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
49.0ms
(* (sin a) (sin b))

simplify5.8s

Calls
83 calls:
Slowest
421.0ms
(* (sqrt r) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
341.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
336.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
329.0ms
(/ (* (* (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)))))
322.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite636.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
40×cos-mult sin-mult
35×add-cbrt-cube pow-prod-down add-exp-log
34×associate-*r*
32×associate-/r/
27×add-sqr-sqrt
25×times-frac
23×associate-*r/
22×*-un-lft-identity associate-*l/ add-cube-cbrt
18×frac-times prod-exp frac-sub cbrt-unprod
10×sub-div
8×pow-sqr pow-prod-up
7×difference-of-squares
5×associate-*l*
4×associate-/r* pow-plus insert-posit16 add-log-exp
3×*-commutative associate-/l*
2×pow2 cbrt-undiv flip3-- swap-sqr div-exp div-inv flip-- unswap-sqr
1×clear-num frac-2neg
Calls
4 calls:
Slowest
398.0ms
(* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
110.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
70.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
54.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

series730.0ms

Calls
4 calls:
Slowest
384.0ms
(* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
196.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
79.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
71.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify25.8s

Calls
170 calls:
Slowest
864.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
837.0ms
(- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))
801.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
742.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
641.0ms
(* (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))))

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes322.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch4.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
3.7s2880×body1280valid
1.7s1861×body640valid
803.0ms752×body320valid
357.0ms2131×body80valid
132.0ms378×body160valid