Details

Time bar (total: 33.4s)

sample580.0ms

Algorithm
intervals
Results
233.0ms92×body1280valid
46.0ms25×body320valid
39.0ms58×body640valid
11.0ms69×body80valid
4.0ms12×body160valid

simplify102.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
101.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune59.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize69.0ms

Local error

Found 3 expressions with local error:

4.1b
(cos (+ a b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite82.0ms

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×expm1-log1p-u associate-/r* times-frac associate-*r* associate-*l* insert-posit16 log1p-expm1-u 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
Counts
3 → 56
Calls
3 calls:
Slowest
32.0ms
(cos (+ a b))
28.0ms
(/ (* r (sin b)) (cos (+ a b)))
18.0ms
(* r (sin b))

series276.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
175.0ms
(/ (* r (sin b)) (cos (+ a b)))
55.0ms
(* r (sin b))
47.0ms
(cos (+ a b))

simplify1.7s

Counts
33 → 65
Calls
33 calls:
Slowest
352.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
296.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
238.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
233.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
225.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune734.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

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))

rewrite94.0ms

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
40.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
29.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
16.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series530.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
324.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
100.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
60.0ms
(* (sin a) (sin b))
46.0ms
(* r (sin b))

simplify4.6s

Counts
56 → 102
Calls
56 calls:
Slowest
776.0ms
(/ (* (* (* 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)))))
506.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
450.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
312.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
310.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

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)))

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×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
87.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
37.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms
(* (sin a) (sin b))

series692.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
174.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
127.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
63.0ms
(* (sin a) (sin b))

simplify6.2s

Counts
86 → 126
Calls
86 calls:
Slowest
477.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
377.0ms
(/ (* (* (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)))))
360.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
360.0ms
(* (* (* 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))))))
352.0ms
(+ (* (* (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

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
19×times-frac
16×associate-*r*
13×add-cbrt-cube add-exp-log
8×pow1
6×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* prod-exp cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num frac-2neg associate-*r/ fma-udef sin-mult
Counts
4 → 98
Calls
4 calls:
Slowest
12.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
11.0ms
(* (sin a) (sin b))
10.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series654.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
323.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
176.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
98.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
57.0ms
(* (sin a) (sin b))

simplify4.5s

Counts
73 → 110
Calls
73 calls:
Slowest
443.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
342.0ms
(* (* (* r r) r) (* (* (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))) (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))))
312.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
285.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
282.0ms
(* (* (* r r) r) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes278.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.1s2930×body1280valid
1.5s1849×body640valid
912.0ms771×body320valid
375.0ms2131×body80valid
144.0ms322×body160valid