Details

Time bar (total: 35.0s)

sample515.0ms

Algorithm
intervals
Results
219.0ms82×body1280valid
59.0ms67×body640valid
41.0ms15×body160valid
20.0ms27×body320valid
12.0ms65×body80valid

simplify68.0ms

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: 15.7b

localize58.0ms

Local error

Found 3 expressions with local error:

3.6b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite52.0ms

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
18.0ms
(cos (+ a b))
17.0ms
(/ (sin b) (cos (+ a b)))
15.0ms
(* r (/ (sin b) (cos (+ a b))))

series257.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
151.0ms
(* r (/ (sin b) (cos (+ a b))))
66.0ms
(/ (sin b) (cos (+ a b)))
37.0ms
(cos (+ a b))

simplify2.4s

Counts
60 → 85
Calls
60 calls:
Slowest
426.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
268.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
264.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
253.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
248.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune978.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

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)))

rewrite188.0ms

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
102.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
33.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms
(* (sin a) (sin b))

series645.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
311.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
160.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
110.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
65.0ms
(* (sin a) (sin b))

simplify6.3s

Counts
86 → 126
Calls
86 calls:
Slowest
454.0ms
(* (* (* 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)))))
401.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
392.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
379.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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)))

rewrite82.0ms

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
32.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
30.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series604.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
333.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
128.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
75.0ms
(* (sin a) (sin b))
69.0ms
(* r (sin b))

simplify4.0s

Counts
56 → 102
Calls
56 calls:
Slowest
484.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
337.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
331.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
318.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
312.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

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))

rewrite79.0ms

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
35.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
19.0ms
(* (/ (cos b) (sin b)) (cos a))
15.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
9.0ms
(/ (cos b) (sin b))

series516.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
275.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
134.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
77.0ms
(* (/ (cos b) (sin b)) (cos a))
31.0ms
(/ (cos b) (sin b))

simplify4.9s

Counts
97 → 128
Calls
97 calls:
Slowest
411.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
363.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
325.0ms
(/ (* (* 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))))
313.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
261.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes290.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.4s2906×body1280valid
2.0s1876×body640valid
507.0ms794×body320valid
374.0ms2071×body80valid
133.0ms357×body160valid