Details

Time bar (total: 35.4s)

sample560.0ms

Algorithm
intervals
Results
231.0ms62×body640valid
188.0ms89×body1280valid
17.0ms73×body80valid
15.0ms21×body320valid
5.0ms11×body160valid

simplify102.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
101.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize64.0ms

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))

rewrite44.0ms

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
Counts
3 → 50
Calls
3 calls:
Slowest
18.0ms
(cos (+ a b))
16.0ms
(/ (* r (sin b)) (cos (+ a b)))
8.0ms
(* r (sin b))

series241.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
151.0ms
(/ (* r (sin b)) (cos (+ a b)))
57.0ms
(* r (sin b))
33.0ms
(cos (+ a b))

simplify1.8s

Counts
33 → 59
Calls
33 calls:
Slowest
276.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
259.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
257.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
205.0ms
(- (log (* r (sin b))) (log (cos (+ a b))))
199.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune731.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

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)))

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×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*
Counts
4 → 80
Calls
4 calls:
Slowest
53.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms
(* (sin a) (sin b))
20.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms
(* r (sin b))

series579.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
310.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
134.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
73.0ms
(* (sin a) (sin b))
62.0ms
(* r (sin b))

simplify3.6s

Counts
53 → 92
Calls
53 calls:
Slowest
326.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
308.0ms
(* (* (* (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))))
305.0ms
(/ (* (* (* 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)))))
287.0ms
(/ (* (* (* 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)))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

26.3b
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))

rewrite436.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
29×sin-mult
23×add-cbrt-cube add-exp-log
18×pow-prod-down
14×cbrt-div
11×frac-times associate-*l/
10×add-sqr-sqrt prod-exp cbrt-unprod
9×associate-/r/
8×*-un-lft-identity add-cube-cbrt
7×associate-*r/ cos-mult frac-sub
4×associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16 add-log-exp
3×associate-/r* times-frac
2×cbrt-undiv pow-plus div-exp *-commutative
1×cbrt-prod pow2 clear-num frac-2neg flip3-- pow1/3 swap-sqr pow3 rem-cbrt-cube div-inv flip-- associate-/l* unswap-sqr
Counts
4 → 107
Calls
4 calls:
Slowest
184.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
178.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
49.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
22.0ms
(* (sin a) (sin b))

series977.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
449.0ms
(* (sin a) (sin b))
354.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
87.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
87.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

simplify9.9s

Counts
91 → 119
Calls
91 calls:
Slowest
747.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
647.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
426.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
402.0ms
(- (+ (log r) (log (sin b))) (log (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))))
382.0ms
(- (log (* r (sin b))) (log (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))))

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

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

rewrite84.0ms

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*
Counts
4 → 80
Calls
4 calls:
Slowest
37.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
17.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
15.0ms
(* (sin b) (sin a))
15.0ms
(* r (sin b))

series591.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
357.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
123.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
67.0ms
(* (sin b) (sin a))
44.0ms
(* r (sin b))

simplify3.5s

Counts
53 → 92
Calls
53 calls:
Slowest
376.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- b a)) (cos (+ b a)))))
328.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))
325.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (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)))))
284.0ms
(/ (* (* (* 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)))))
283.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes448.0ms

Accuracy

0% (0.3b remaining)

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

bsearch8.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
3.8s2974×body1280valid
1.9s1769×body640valid
773.0ms2126×body80valid
561.0ms764×body320valid
164.0ms368×body160valid