Details

Time bar (total: 37.7s)

sample415.0ms

Algorithm
intervals
Results
196.0ms79×body1280valid
61.0ms62×body640valid
55.0ms79×body80valid
34.0ms11×body160valid
20.0ms25×body320valid

simplify170.0ms

Calls
1 calls:
Slowest
169.0ms
(* r (/ (sin b) (cos (+ a b))))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize40.0ms

Local error

Found 3 expressions with local error:

3.0b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite79.0ms

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
Calls
3 calls:
Slowest
30.0ms
(cos (+ a b))
25.0ms
(* r (/ (sin b) (cos (+ a b))))
18.0ms
(/ (sin b) (cos (+ a b)))

series257.0ms

Calls
3 calls:
Slowest
161.0ms
(* r (/ (sin b) (cos (+ a b))))
53.0ms
(/ (sin b) (cos (+ a b)))
42.0ms
(cos (+ a b))

simplify2.5s

Calls
60 calls:
Slowest
419.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
352.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
317.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
245.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
206.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune919.0ms

Pruning

10 alts after pruning (10 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)))

rewrite189.0ms

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/
Calls
4 calls:
Slowest
89.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
23.0ms
(* (sin a) (sin b))

series715.0ms

Calls
4 calls:
Slowest
338.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
157.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
146.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
74.0ms
(* (sin a) (sin b))

simplify6.0s

Calls
86 calls:
Slowest
447.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
346.0ms
(* (* (* 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))))))
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)))))
327.0ms
(/ (* (* (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)))))
317.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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
Calls
4 calls:
Slowest
15.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
11.0ms
(* (sin a) (sin b))
9.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series655.0ms

Calls
4 calls:
Slowest
304.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
157.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
126.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
68.0ms
(* (sin a) (sin b))

simplify4.9s

Calls
73 calls:
Slowest
399.0ms
(/ (* (* (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))))))
384.0ms
(* (* (* 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)))))))
354.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
340.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
268.0ms
(* (* (* 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)))))))

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
0.1b
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
19×times-frac
18×associate-*r*
13×add-cbrt-cube add-exp-log
8×pow1
7×add-log-exp
6×associate-*l*
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u
3×associate-/r* flip3-- prod-diff prod-exp cbrt-unprod flip-- associate-/l* unswap-sqr
2×cbrt-undiv diff-log div-exp pow-prod-down *-commutative div-inv
1×log1p-udef clear-num sub-neg frac-2neg fma-neg associate-*r/ sin-mult
Calls
4 calls:
Slowest
63.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
46.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
22.0ms
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
14.0ms
(* (sin a) (sin b))

series814.0ms

Calls
4 calls:
Slowest
373.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
197.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
167.0ms
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
76.0ms
(* (sin a) (sin b))

simplify6.8s

Calls
86 calls:
Slowest
700.0ms
(/ (exp (* (cos a) (cos b))) (exp (log1p (expm1 (* (sin a) (sin b))))))
369.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))) (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))) (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))))
352.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
335.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
331.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log1p (expm1 (* (sin a) (sin b)))) (log1p (expm1 (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes341.0ms

Accuracy

0% (0.3b remaining)

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

bsearch7.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.6s2880×body1280valid
1.6s1861×body640valid
437.0ms752×body320valid
425.0ms2131×body80valid
160.0ms378×body160valid