Details

Time bar (total: 31.3s)

sample528.0ms

Algorithm
intervals
Results
275.0ms98×body1280valid
96.0ms62×body640valid
40.0ms69×body80valid
12.0ms18×body320valid
4.0ms9×body160valid

simplify135.0ms

Calls
1 calls:
Slowest
134.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize74.0ms

Local error

Found 3 expressions with local error:

2.8b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite104.0ms

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
61.0ms
(/ (* r (sin b)) (cos (+ a b)))
22.0ms
(cos (+ a b))
18.0ms
(* r (sin b))

series262.0ms

Calls
3 calls:
Slowest
147.0ms
(/ (* r (sin b)) (cos (+ a b)))
61.0ms
(cos (+ a b))
54.0ms
(* r (sin b))

simplify1.3s

Calls
33 calls:
Slowest
258.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
195.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
192.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
177.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
153.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune640.0ms

Pruning

8 alts after pruning (8 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
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b
(* r (sin b))

rewrite133.0ms

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
60.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
33.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
22.0ms
(* (sin a) (sin b))
16.0ms
(* r (sin b))

series572.0ms

Calls
4 calls:
Slowest
326.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
105.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
71.0ms
(* (sin a) (sin b))
70.0ms
(* r (sin b))

simplify3.7s

Calls
53 calls:
Slowest
338.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
323.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
316.0ms
(/ (* (* (* 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)))))
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)))))
303.0ms
(/ (* (* (* 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)))))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite224.0ms

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
119.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
51.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
29.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
22.0ms
(* (sin a) (sin b))

series650.0ms

Calls
4 calls:
Slowest
317.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
168.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
107.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms
(* (sin a) (sin b))

simplify5.9s

Calls
83 calls:
Slowest
451.0ms
(+ (log r) (- (log (sin b)) (log (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
394.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
339.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
322.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
321.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity times-frac add-cube-cbrt
13×add-cbrt-cube associate-*l* add-exp-log
6×pow1 associate-/r* associate-/l* add-log-exp
4×insert-posit16
3×cbrt-undiv div-exp associate-*r* div-inv
2×clear-num frac-2neg flip3-- prod-exp associate-/r/ cbrt-unprod flip-- unswap-sqr
1×sub-neg diff-log pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
27.0ms
(* (/ (cos b) (sin b)) (cos a))
24.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
15.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
11.0ms
(/ (cos b) (sin b))

series518.0ms

Calls
4 calls:
Slowest
260.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
121.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
100.0ms
(* (/ (cos b) (sin b)) (cos a))
37.0ms
(/ (cos b) (sin b))

simplify4.1s

Calls
90 calls:
Slowest
427.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
312.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
307.0ms
(/ (* (* 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))))
268.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
257.0ms
(- (/ 1 b) (+ (* 1/2 (/ (pow a 2) b)) (* 1/3 b)))

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes298.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.2s2948×body1280valid
1.9s1840×body640valid
447.0ms782×body320valid
403.0ms2096×body80valid
150.0ms336×body160valid