Details

Time bar (total: 35.3s)

sample343.0ms

Algorithm
intervals
Results
177.0ms87×body1280valid
63.0ms70×body640valid
16.0ms23×body320valid
13.0ms63×body80valid
6.0ms13×body160valid

simplify113.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
112.0ms
(* r (/ (sin b) (cos (+ a b))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize35.0ms

Local error

Found 3 expressions with local error:

3.2b
(cos (+ a b))
0.3b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×associate-/r* associate-*l* insert-posit16 associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 70
Calls
3 calls:
Slowest
26.0ms
(* r (/ (sin b) (cos (+ a b))))
18.0ms
(/ (sin b) (cos (+ a b)))
17.0ms
(cos (+ a b))

series248.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
137.0ms
(* r (/ (sin b) (cos (+ a b))))
70.0ms
(/ (sin b) (cos (+ a b)))
41.0ms
(cos (+ a b))

simplify2.4s

Counts
60 → 79
Calls
60 calls:
Slowest
457.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
350.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
263.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
232.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
178.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune938.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (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)))

rewrite159.0ms

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/
Counts
4 → 104
Calls
4 calls:
Slowest
90.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
42.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms
(* (sin a) (sin b))

series708.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
323.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
175.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
148.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
62.0ms
(* (sin a) (sin b))

simplify5.5s

Counts
83 → 116
Calls
83 calls:
Slowest
375.0ms
(/ (* (* (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)))))
348.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
337.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
325.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
306.0ms
(* (* (* 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))))))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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

rewrite72.0ms

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
Counts
4 → 104
Calls
4 calls:
Slowest
28.0ms
(* (/ (cos b) (sin b)) (cos a))
19.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
13.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
10.0ms
(/ (cos b) (sin b))

series528.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
271.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
117.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
113.0ms
(* (/ (cos b) (sin b)) (cos a))
27.0ms
(/ (cos b) (sin b))

simplify3.9s

Counts
90 → 116
Calls
90 calls:
Slowest
358.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
295.0ms
(/ (* (* 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))))
282.0ms
(+ (* (* (/ (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
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
238.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* (sin a) (sin b))
0.2b
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube associate-*r*
18×times-frac
13×prod-exp
12×pow1
8×associate-/r/
7×cbrt-unprod sin-mult
6×div-exp cos-mult add-log-exp
4×associate-*l* pow-prod-down insert-posit16
3×cbrt-undiv rec-exp associate-/r* flip3-- 1-exp frac-sub flip-- associate-/l* sub-div
2×*-commutative div-inv
1×clear-num sub-neg frac-2neg diff-log associate-*r/ un-div-inv pow-flip inv-pow unswap-sqr
Counts
4 → 114
Calls
4 calls:
Slowest
93.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms
(* (sin a) (sin b))

series633.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
312.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
151.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
109.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
60.0ms
(* (sin a) (sin b))

simplify6.9s

Counts
89 → 126
Calls
89 calls:
Slowest
314.0ms
(* (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (/ (* (* 1 1) 1) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
307.0ms
(* (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (/ (* (* 1 1) 1) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
304.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
293.0ms
(/ (* (* 1 1) 1) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
279.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes234.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.0s

Algorithm
intervals
Results
4.1s2921×body1280valid
1.7s1775×body640valid
429.0ms2156×body80valid
418.0ms796×body320valid
117.0ms353×body160valid