Details

Time bar (total: 34.1s)

sample339.0ms

Algorithm
intervals
Results
90.0ms82×body1280valid
63.0ms27×body320valid
52.0ms67×body640valid
10.0ms65×body80valid
5.0ms15×body160valid

simplify30.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
30.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize52.0ms

Local error

Found 3 expressions with local error:

3.6b
(cos (+ a b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite58.0ms

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
23.0ms
(/ (* r (sin b)) (cos (+ a b)))
16.0ms
(cos (+ a b))
16.0ms
(* r (sin b))

series251.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
156.0ms
(/ (* r (sin b)) (cos (+ a b)))
67.0ms
(* r (sin b))
28.0ms
(cos (+ a b))

simplify1.7s

Counts
33 → 65
Calls
33 calls:
Slowest
372.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
254.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
254.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
214.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
192.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune796.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

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
44.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
24.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
13.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series573.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
348.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
112.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms
(* (sin a) (sin b))
44.0ms
(* r (sin b))

simplify4.1s

Counts
56 → 102
Calls
56 calls:
Slowest
485.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
368.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
320.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
315.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
291.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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)))

rewrite235.0ms

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
140.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
37.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
33.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms
(* (sin a) (sin b))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
661.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
187.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
137.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms
(* (sin a) (sin b))

simplify6.3s

Counts
86 → 126
Calls
86 calls:
Slowest
424.0ms
(* (* (* 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))))))
412.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
407.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
389.0ms
(/ (* (* (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)))))
363.0ms
(+ (* (* (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

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

rewrite106.0ms

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
48.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
31.0ms
(* (/ (cos b) (sin b)) (cos a))
16.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
10.0ms
(/ (cos b) (sin b))

series586.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
312.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
128.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
110.0ms
(* (/ (cos b) (sin b)) (cos a))
35.0ms
(/ (cos b) (sin b))

simplify5.0s

Counts
97 → 128
Calls
97 calls:
Slowest
398.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
351.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
342.0ms
(/ (* (* 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))))
280.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
274.0ms
(/ (exp (* (/ (cos b) (sin b)) (cos a))) (exp (sin a)))

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes255.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.6s2906×body1280valid
1.6s1876×body640valid
520.0ms794×body320valid
426.0ms2071×body80valid
169.0ms357×body160valid