Details

Time bar (total: 1.0m)

sample314.0ms

Algorithm
intervals
Results
162.0ms98×body1280valid
46.0ms51×body640valid
19.0ms29×body320valid
17.0ms70×body80valid
3.0ms8×body160valid

simplify59.0ms

Calls
1 calls:
Slowest
59.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize18.0ms

Local error

Found 3 expressions with local error:

2.9b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
36×times-frac
30×*-un-lft-identity add-cube-cbrt
15×associate-*r* associate-*l*
12×associate-/l*
10×add-cbrt-cube add-exp-log
5×pow1 *-commutative unswap-sqr
3×associate-/r* insert-posit16 add-log-exp
2×cbrt-undiv cos-sum div-exp prod-exp cbrt-unprod
1×+-commutative clear-num frac-2neg pow-prod-down div-inv
Calls
3 calls:
Slowest
32.0ms
(/ (* r (sin b)) (cos (+ a b)))
18.0ms
(cos (+ a b))
15.0ms
(* r (sin b))

series238.0ms

Calls
3 calls:
Slowest
150.0ms
(/ (* r (sin b)) (cos (+ a b)))
47.0ms
(* r (sin b))
41.0ms
(cos (+ a b))

simplify3.7s

Calls
109 calls:
Slowest
325.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
241.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
241.0ms
(/ (* r (* (cbrt (sin b)) (cbrt (sin b)))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))
221.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
183.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
253×add-sqr-sqrt
169×*-un-lft-identity
132×times-frac
98×associate-*l*
70×unswap-sqr
57×add-cube-cbrt
56×distribute-lft-out-- difference-of-squares
42×associate-*r*
14×*-commutative
13×add-cbrt-cube add-exp-log
12×associate-/l*
11×associate-/r*
8×pow1
6×add-log-exp
5×sin-mult
4×associate-/r/ cos-mult insert-posit16
3×prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down frac-sub flip-- sub-div
1×clear-num sub-neg frac-2neg diff-log div-inv
Calls
4 calls:
Slowest
105.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
83.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms
(* (sin a) (sin b))
16.0ms
(* r (sin b))

series534.0ms

Calls
4 calls:
Slowest
305.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
104.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
81.0ms
(* (sin a) (sin b))
44.0ms
(* r (sin b))

simplify18.3s

Calls
340 calls:
Slowest
404.0ms
(/ (* r (sqrt (sin b))) 1)
361.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
329.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
323.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
314.0ms
(/ (* (* (* 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)))))

prune3.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

27.5b
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
0.2b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(* (sin a) (sin b))
0.2b
(* (sin a) (sin b))

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
108×associate-*l*
82×cbrt-prod
74×unswap-sqr
69×associate-*r*
47×pow1
45×*-un-lft-identity
37×add-cube-cbrt
32×swap-sqr
20×add-cbrt-cube add-exp-log
19×pow-prod-down
18×sin-mult
17×*-commutative
10×prod-exp cbrt-unprod
7×cbrt-div
6×frac-times associate-*l/
4×associate-*r/ pow-sqr pow-prod-up insert-posit16 add-log-exp
2×pow-plus pow3 rem-cbrt-cube
1×pow2 pow1/3
Calls
4 calls:
Slowest
254.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
122.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
11.0ms
(* (sin a) (sin b))
11.0ms
(* (sin a) (sin b))

series282.0ms

Calls
4 calls:
Slowest
85.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
73.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
63.0ms
(* (sin a) (sin b))
61.0ms
(* (sin a) (sin b))

simplify12.4s

Calls
216 calls:
Slowest
821.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
730.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
357.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
335.0ms
(cbrt (* (* (- (cos (- a b)) (cos (+ a b))) (- (cos (- a b)) (cos (+ a b)))) (- (cos (- a b)) (cos (+ a b)))))
309.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (cbrt (* (sin a) (sin b))) (cbrt (* (sin a) (sin b))))))

prune3.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
85×add-sqr-sqrt
55×*-un-lft-identity
48×times-frac
35×add-cube-cbrt
18×associate-*l*
15×difference-of-squares
14×associate-/r*
13×add-cbrt-cube add-exp-log
12×unswap-sqr
10×distribute-lft-out--
9×associate-*l/ associate-/l*
6×pow1 add-log-exp
4×insert-posit16
3×cbrt-undiv clear-num frac-2neg div-exp associate-*r* div-inv
2×flip3-- prod-exp associate-/r/ cbrt-unprod flip--
1×sub-neg diff-log pow-prod-down *-commutative
Calls
4 calls:
Slowest
101.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
87.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
20.0ms
(* (/ (cos b) (sin b)) (cos a))
8.0ms
(/ (cos b) (sin b))

series495.0ms

Calls
4 calls:
Slowest
239.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
133.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
90.0ms
(* (/ (cos b) (sin b)) (cos a))
34.0ms
(/ (cos b) (sin b))

simplify5.9s

Calls
141 calls:
Slowest
424.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
325.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
308.0ms
(/ (* (* r r) r) (* (* (- (* (/ (cos b) (sin b)) (cos a)) (sin a)) (- (* (/ (cos b) (sin b)) (cos a)) (sin a))) (- (* (/ (cos b) (sin b)) (cos a)) (sin a))))
307.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
275.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes320.0ms

Accuracy

0% (0.4b remaining)

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

bsearch2.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.0s3020×body1280valid
1.5s1778×body640valid
932.0ms2079×body80valid
876.0ms792×body320valid
158.0ms332×body160valid