Details

Time bar (total: 33.8s)

sample265.0ms

Algorithm
intervals
Results
135.0ms92×body1280valid
48.0ms62×body640valid
15.0ms25×body320valid
11.0ms64×body80valid
5.0ms13×body160valid

simplify438.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
438.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize19.0ms

Local error

Found 3 expressions with local error:

2.5b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite41.0ms

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
19.0ms
(* r (sin b))
12.0ms
(/ (* r (sin b)) (cos (+ a b)))
9.0ms
(cos (+ a b))

series213.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
133.0ms
(/ (* r (sin b)) (cos (+ a b)))
55.0ms
(* r (sin b))
25.0ms
(cos (+ a b))

simplify1.5s

Counts
33 → 65
Calls
33 calls:
Slowest
313.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
254.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
220.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
216.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
212.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune653.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize62.0ms

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)))

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×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
54.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
34.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
23.0ms
(* (sin a) (sin b))
21.0ms
(* r (sin b))

series585.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
331.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
146.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
64.0ms
(* (sin a) (sin b))
44.0ms
(* r (sin b))

simplify4.0s

Counts
56 → 102
Calls
56 calls:
Slowest
438.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
374.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
333.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
328.0ms
(+ (* (* (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)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×*-un-lft-identity add-cube-cbrt
28×times-frac
13×add-cbrt-cube associate-*l* add-exp-log
6×pow1 associate-/r* associate-/l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp associate-*r* prod-diff div-inv
2×clear-num frac-2neg flip3-- prod-exp associate-/r/ cbrt-unprod flip-- unswap-sqr
1×sub-neg fma-neg diff-log pow-prod-down associate-*l/ *-commutative
Counts
4 → 116
Calls
4 calls:
Slowest
44.0ms
(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
30.0ms
(* (/ (cos a) (sin b)) (cos b))
19.0ms
(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
17.0ms
(/ (cos a) (sin b))

series544.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
263.0ms
(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
127.0ms
(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
90.0ms
(* (/ (cos a) (sin b)) (cos b))
64.0ms
(/ (cos a) (sin b))

simplify5.1s

Counts
97 → 128
Calls
97 calls:
Slowest
419.0ms
(/ (* (* (cos a) (cos a)) (cos a)) (* (* (sin b) (sin b)) (sin b)))
340.0ms
(+ (* (* (/ (cos a) (sin b)) (cos b)) (* (/ (cos a) (sin b)) (cos b))) (+ (* (sin a) (sin a)) (* (* (/ (cos a) (sin b)) (cos b)) (sin a))))
302.0ms
(/ (* (* r r) r) (* (* (- (* (/ (cos a) (sin b)) (cos b)) (sin a)) (- (* (/ (cos a) (sin b)) (cos b)) (sin a))) (- (* (/ (cos a) (sin b)) (cos b)) (sin a))))
263.0ms
(- (/ 1 b) (+ (* 1/3 b) (* 1/2 (/ (pow a 2) b))))
253.0ms
(- (+ (/ 1 b) (* 1/6 b)) (* 1/2 (/ (pow a 2) b)))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
39×times-frac
37×*-un-lft-identity
36×add-cube-cbrt
24×add-exp-log
18×add-cbrt-cube associate-*r*
16×associate-*l*
9×pow1
6×associate-/r* div-exp prod-exp associate-/l*
5×unswap-sqr
4×expm1-log1p-u cbrt-undiv associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
2×rec-exp clear-num frac-2neg flip3-- 1-exp pow-prod-down *-commutative flip--
1×associate-*l/ associate-*r/ un-div-inv pow-flip inv-pow
Counts
4 → 142
Calls
4 calls:
Slowest
107.0ms
(* r (/ 1 (- (* (/ (cos a) (sin b)) (cos b)) (sin a))))
31.0ms
(/ 1 (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
18.0ms
(* (/ (cos a) (sin b)) (cos b))
9.0ms
(/ (cos a) (sin b))

series620.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(* r (/ 1 (- (* (/ (cos a) (sin b)) (cos b)) (sin a))))
142.0ms
(/ 1 (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
111.0ms
(* (/ (cos a) (sin b)) (cos b))
74.0ms
(/ (cos a) (sin b))

simplify6.8s

Counts
123 → 154
Calls
123 calls:
Slowest
535.0ms
(* (* (* r r) r) (/ (* (* 1 1) 1) (* (* (- (* (/ (cos a) (sin b)) (cos b)) (sin a)) (- (* (/ (cos a) (sin b)) (cos b)) (sin a))) (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))))
436.0ms
(/ (* (* (cos a) (cos a)) (cos a)) (* (* (sin b) (sin b)) (sin b)))
300.0ms
(* (* (* (/ (cos a) (sin b)) (/ (cos a) (sin b))) (/ (cos a) (sin b))) (* (* (cos b) (cos b)) (cos b)))
274.0ms
(+ (* (* (/ (cos a) (sin b)) (cos b)) (* (/ (cos a) (sin b)) (cos b))) (+ (* (sin a) (sin a)) (* (* (/ (cos a) (sin b)) (cos b)) (sin a))))
264.0ms
(- (/ 1 b) (+ (* 1/3 b) (* 1/2 (/ (pow a 2) b))))

prune1.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes289.0ms

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
3.6s2836×body1280valid
2.4s1887×body640valid
504.0ms784×body320valid
451.0ms2162×body80valid
201.0ms333×body160valid