Details

Time bar (total: 31.2s)

sample247.0ms

Algorithm
intervals
Results
87.0ms89×body1280valid
46.0ms67×body80valid
37.0ms63×body640valid
10.0ms26×body320valid
3.0ms11×body160valid

simplify84.0ms

Calls
1 calls:
Slowest
83.0ms
(* r (/ (sin b) (cos (+ a b))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize18.0ms

Local error

Found 3 expressions with local error:

2.9b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
5×add-cbrt-cube add-exp-log
3×pow1 associate-/r* insert-posit16 associate-/l* add-log-exp
2×div-inv
1×cbrt-undiv cos-sum clear-num frac-2neg div-exp associate-*r/ *-commutative
Calls
3 calls:
Slowest
5.0ms
(/ (sin b) (cos (+ a b)))
3.0ms
(cos (+ a b))
3.0ms
(* r (/ (sin b) (cos (+ a b))))

series223.0ms

Calls
3 calls:
Slowest
131.0ms
(* r (/ (sin b) (cos (+ a b))))
49.0ms
(/ (sin b) (cos (+ a b)))
43.0ms
(cos (+ a b))

simplify1.2s

Calls
49 calls:
Slowest
237.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
194.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
166.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
149.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
48.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))

prune686.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

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)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×associate-*r*
18×times-frac
8×add-cbrt-cube add-exp-log associate-/r/
7×sin-mult
6×pow1 cos-mult add-log-exp
4×insert-posit16
3×associate-/r* flip3-- associate-*l* frac-sub flip-- associate-/l* sub-div
2×*-commutative div-inv
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp pow-prod-down prod-exp associate-*r/ cbrt-unprod
Calls
4 calls:
Slowest
27.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
26.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms
(* (sin a) (sin b))

series556.0ms

Calls
4 calls:
Slowest
283.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
122.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
89.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
62.0ms
(* (sin a) (sin b))

simplify3.7s

Calls
70 calls:
Slowest
315.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
295.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
260.0ms
(/ (* (* (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)))))
258.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
250.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
13×associate-*l*
11×add-cbrt-cube add-exp-log
6×pow1 associate-/r* add-log-exp
4×insert-posit16
3×associate-*r* div-inv associate-/l*
2×cbrt-undiv clear-num frac-2neg flip3-- div-exp prod-exp associate-/r/ cbrt-unprod flip--
1×sub-neg diff-log pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
14.0ms
(* (/ (cos b) (sin b)) (cos a))
11.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
8.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
4.0ms
(/ (cos b) (sin b))

series457.0ms

Calls
4 calls:
Slowest
223.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
122.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
83.0ms
(* (/ (cos b) (sin b)) (cos a))
28.0ms
(/ (cos b) (sin b))

simplify2.8s

Calls
64 calls:
Slowest
458.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
281.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
253.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))
219.0ms
(- (/ 1 b) (+ (* 1/2 (/ (pow a 2) b)) (* 1/3 b)))
205.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))

prune1.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

24.0b
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
0.3b
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
0.2b
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
0.2b
(* (sin b) (sin a))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1
29×sin-mult
20×add-cbrt-cube add-exp-log
14×add-sqr-sqrt cbrt-div *-un-lft-identity pow-prod-down add-cube-cbrt
11×frac-times associate-*l/
9×times-frac prod-exp associate-/r/ cbrt-unprod
7×associate-*r/ cos-mult frac-sub
4×associate-*r* associate-*l* pow-prod-up insert-posit16 add-log-exp
3×associate-/r* associate-/l*
2×pow-plus *-commutative
1×cbrt-prod pow2 cbrt-undiv clear-num frac-2neg flip3-- pow1/3 div-exp pow3 rem-cbrt-cube div-inv flip--
Calls
4 calls:
Slowest
82.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
67.0ms
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
21.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
4.0ms
(* (sin b) (sin a))

series302.0ms

Calls
4 calls:
Slowest
131.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
64.0ms
(* (sin b) (sin a))
53.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
53.0ms
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))

simplify8.0s

Calls
91 calls:
Slowest
541.0ms
(* (* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a))) (* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a))))
337.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))))) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))))))
335.0ms
(cbrt (* (* (- (cos (- b a)) (cos (+ b a))) (- (cos (- b a)) (cos (+ b a)))) (- (cos (- b a)) (cos (+ b a)))))
307.0ms
(- (* (pow a 2) (pow b 2)) (+ (* 1/3 (* (pow a 2) (pow b 4))) (* 1/3 (* (pow a 4) (pow b 2)))))
305.0ms
(cbrt (* (* (* (sin b) (sin a)) (- (cos (- b a)) (cos (+ b a)))) (- (cos (- b a)) (cos (+ b a)))))

prune1.9s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

regimes421.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.5s2864×body1280valid
1.6s1846×body640valid
485.0ms743×body320valid
423.0ms2172×body80valid
130.0ms376×body160valid