Details

Time bar (total: 35.6s)

sample307.0ms

Algorithm
intervals
Results
117.0ms92×body1280valid
37.0ms58×body640valid
18.0ms25×body320valid
9.0ms69×body80valid
3.0ms12×body160valid

simplify69.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
68.0ms
(* r (/ (sin b) (cos (+ a b))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize37.0ms

Local error

Found 3 expressions with local error:

4.1b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite62.0ms

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
23.0ms
(* r (/ (sin b) (cos (+ a b))))
18.0ms
(cos (+ a b))
17.0ms
(/ (sin b) (cos (+ a b)))

series227.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
105.0ms
(* r (/ (sin b) (cos (+ a b))))
81.0ms
(/ (sin b) (cos (+ a b)))
41.0ms
(cos (+ a b))

simplify2.3s

Counts
60 → 79
Calls
60 calls:
Slowest
424.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
323.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
270.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
224.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
177.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune871.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
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)))

rewrite157.0ms

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
77.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
39.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
29.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms
(* (sin a) (sin b))

series718.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
364.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
162.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
134.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms
(* (sin a) (sin b))

simplify5.7s

Counts
83 → 116
Calls
83 calls:
Slowest
408.0ms
(* (* (* 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))))))
390.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
361.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
340.0ms
(/ (* (* (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)))))
327.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

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))

rewrite101.0ms

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
45.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
27.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
16.0ms
(* r (sin b))
11.0ms
(* (sin a) (sin b))

series621.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
352.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
134.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
87.0ms
(* (sin a) (sin b))
47.0ms
(* r (sin b))

simplify3.8s

Counts
53 → 92
Calls
53 calls:
Slowest
375.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
369.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
333.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
333.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
305.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
32×add-sqr-sqrt
24×*-un-lft-identity
23×add-cube-cbrt
22×add-cbrt-cube
21×associate-*r*
20×times-frac
14×pow1 prod-exp
9×associate-*l*
8×associate-/r/ cbrt-unprod
6×div-exp
5×pow-prod-down sin-mult
4×associate-*r/ cos-mult insert-posit16 add-log-exp unswap-sqr
3×cbrt-undiv rec-exp associate-/r* 1-exp *-commutative associate-/l*
2×flip3-- un-div-inv frac-sub div-inv flip-- sub-div
1×clear-num frac-2neg pow-flip inv-pow
Counts
4 → 122
Calls
4 calls:
Slowest
108.0ms
(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
104.0ms
(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
36.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms
(* (sin a) (sin b))

series728.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
333.0ms
(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
169.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
144.0ms
(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
82.0ms
(* (sin a) (sin b))

simplify7.4s

Counts
101 → 134
Calls
101 calls:
Slowest
638.0ms
(* (* (* (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))))))
343.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
299.0ms
(/ (* (* 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)))))
286.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
257.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes298.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch4.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
4.1s2930×body1280valid
1.9s1849×body640valid
423.0ms771×body320valid
407.0ms2131×body80valid
109.0ms322×body160valid