Details

Time bar (total: 33.3s)

sample296.0ms

Algorithm
intervals
Results
134.0ms92×body1280valid
45.0ms58×body640valid
16.0ms25×body320valid
12.0ms69×body80valid
4.0ms12×body160valid

simplify104.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
103.0ms
(* r (/ (sin b) (cos (+ a b))))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize35.0ms

Local error

Found 3 expressions with local error:

4.1b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite65.0ms

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
26.0ms
(* r (/ (sin b) (cos (+ a b))))
19.0ms
(/ (sin b) (cos (+ a b)))
16.0ms
(cos (+ a b))

series211.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
104.0ms
(* r (/ (sin b) (cos (+ a b))))
54.0ms
(/ (sin b) (cos (+ a b)))
53.0ms
(cos (+ a b))

simplify2.4s

Counts
60 → 85
Calls
60 calls:
Slowest
410.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
310.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
285.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
237.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
227.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune944.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

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)))

rewrite182.0ms

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
121.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
26.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms
(* (sin a) (sin b))

series643.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
320.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
139.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
107.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
76.0ms
(* (sin a) (sin b))

simplify6.3s

Counts
86 → 126
Calls
86 calls:
Slowest
486.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
429.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
360.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
359.0ms
(/ (* (* (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)))))
341.0ms
(* (* (* 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))))))

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

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))))

rewrite54.0ms

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
19.0ms
(* (sin a) (sin b))
17.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
15.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series661.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
320.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
148.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
127.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
66.0ms
(* (sin a) (sin b))

simplify4.4s

Counts
73 → 110
Calls
73 calls:
Slowest
379.0ms
(* (* (* 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)))))))
356.0ms
(/ (* (* (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))))))
315.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
293.0ms
(* (* (* 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)))))))
282.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

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
30.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
17.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
11.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series587.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
322.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
111.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
81.0ms
(* (sin a) (sin b))
72.0ms
(* r (sin b))

simplify4.1s

Counts
56 → 102
Calls
56 calls:
Slowest
417.0ms
(+ (log (sin a)) (log (sin b)))
316.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos b) (cos a)) (* (sin a) (sin b)))))
315.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
309.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
299.0ms
(- (* (+ (cos (+ b a)) (cos (- b a))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes270.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
4.0s2930×body1280valid
1.9s1849×body640valid
482.0ms771×body320valid
415.0ms2131×body80valid
118.0ms322×body160valid