Details

Time bar (total: 36.2s)

sample320.0ms

Algorithm
intervals
Results
109.0ms86×body1280valid
83.0ms63×body640valid
15.0ms85×body80valid
9.0ms13×body320valid
4.0ms9×body160valid

simplify67.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
66.0ms
(* r (/ (sin b) (cos (+ a b))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize40.0ms

Local error

Found 3 expressions with local error:

4.6b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite53.0ms

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×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u 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 → 76
Calls
3 calls:
Slowest
27.0ms
(* r (/ (sin b) (cos (+ a b))))
15.0ms
(/ (sin b) (cos (+ a b)))
8.0ms
(cos (+ a b))

series223.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
146.0ms
(* r (/ (sin b) (cos (+ a b))))
46.0ms
(/ (sin b) (cos (+ a b)))
31.0ms
(cos (+ a b))

simplify2.5s

Counts
60 → 85
Calls
60 calls:
Slowest
457.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
328.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
293.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
263.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
197.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune842.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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)))

rewrite198.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u
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 fma-neg diff-log prod-diff associate-*r/
Counts
4 → 114
Calls
4 calls:
Slowest
115.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
36.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
34.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms
(* (sin a) (sin b))

series662.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
326.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
141.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
116.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
78.0ms
(* (sin a) (sin b))

simplify6.7s

Counts
86 → 126
Calls
86 calls:
Slowest
861.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
377.0ms
(* (* (* 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))))))
371.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
348.0ms
(/ (* (* (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)))))
316.0ms
(+ (* (* (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

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

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)))

rewrite96.0ms

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×expm1-log1p-u associate-/r/ cos-mult insert-posit16 log1p-expm1-u
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 fma-neg diff-log prod-diff div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
Slowest
37.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
28.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
22.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series574.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
308.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
151.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
61.0ms
(* (sin a) (sin b))
54.0ms
(* r (sin b))

simplify4.1s

Counts
56 → 102
Calls
56 calls:
Slowest
491.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
334.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
324.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
311.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
308.0ms
(/ (* (* (* 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

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.2b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(* (sin a) (sin b))
0.2b
(* (sin a) (sin b))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
36×pow-prod-down
32×add-cbrt-cube add-exp-log
18×prod-exp cbrt-unprod
12×add-sqr-sqrt
8×*-un-lft-identity associate-*r* associate-*l* pow-sqr pow-prod-up add-cube-cbrt
6×sin-mult
4×expm1-log1p-u pow-plus cos-mult *-commutative insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times swap-sqr associate-*l/ associate-*r/ unswap-sqr
Counts
4 → 124
Calls
4 calls:
Slowest
65.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
45.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
22.0ms
(* (sin a) (sin b))
22.0ms
(* (sin a) (sin b))

series284.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(* (sin a) (sin b))
72.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
66.0ms
(* (sin a) (sin b))
61.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

simplify6.9s

Counts
108 → 136
Calls
108 calls:
Slowest
882.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
814.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
758.0ms
(* (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))))
638.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
350.0ms
(* (* (* (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: 0.0b

regimes240.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.1s2874×body1280valid
1.9s1822×body640valid
512.0ms739×body320valid
422.0ms2164×body80valid
146.0ms403×body160valid