Details

Time bar (total: 27.0s)

sample325.0ms

Algorithm
intervals
Results
125.0ms98×body1280valid
78.0ms62×body640valid
12.0ms69×body80valid
9.0ms18×body320valid
3.0ms9×body160valid

simplify59.0ms

Calls
1 calls:
Slowest
58.0ms
(* r (/ (sin b) (cos (+ a b))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize429.0ms

Local error

Found 3 expressions with local error:

2.8b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.1b
(* r (/ (sin b) (cos (+ a b))))

rewrite26.0ms

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
10.0ms
(/ (sin b) (cos (+ a b)))
7.0ms
(cos (+ a b))
6.0ms
(* r (/ (sin b) (cos (+ a b))))

series225.0ms

Calls
3 calls:
Slowest
131.0ms
(* r (/ (sin b) (cos (+ a b))))
51.0ms
(/ (sin b) (cos (+ a b)))
42.0ms
(cos (+ a b))

simplify1.3s

Calls
49 calls:
Slowest
310.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
186.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
159.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
117.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
66.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))

prune774.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

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
29.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
14.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms
(* (sin a) (sin b))

series664.0ms

Calls
4 calls:
Slowest
297.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
200.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
107.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
60.0ms
(* (sin a) (sin b))

simplify3.9s

Calls
70 calls:
Slowest
321.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
313.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
280.0ms
(/ (* (* (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)))))
273.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
255.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize21.0ms

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))

rewrite55.0ms

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
19.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
14.0ms
(* (/ (cos b) (sin b)) (cos a))
12.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
8.0ms
(/ (cos b) (sin b))

series532.0ms

Calls
4 calls:
Slowest
301.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
119.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
82.0ms
(* (/ (cos b) (sin b)) (cos a))
31.0ms
(/ (cos b) (sin b))

simplify2.7s

Calls
64 calls:
Slowest
376.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
286.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
254.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))
236.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
203.0ms
(- (/ 1 b) (+ (* 1/2 (/ (pow a 2) b)) (* 1/3 b)))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* (sin a) (sin b))
0.2b
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
11×associate-*r* add-exp-log
9×pow1
8×add-sqr-sqrt *-un-lft-identity add-cbrt-cube associate-/r/ add-cube-cbrt
7×sin-mult
6×cos-mult add-log-exp
4×associate-*l* insert-posit16
3×associate-/r* flip3-- prod-exp frac-sub flip-- sub-div
2×rec-exp pow-prod-down *-commutative cbrt-unprod div-inv
1×clear-num sub-neg frac-2neg diff-log associate-*r/ un-div-inv pow-flip inv-pow
Calls
4 calls:
Slowest
27.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
20.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms
(* (sin a) (sin b))

series600.0ms

Calls
4 calls:
Slowest
335.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
124.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
87.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
54.0ms
(* (sin a) (sin b))

simplify3.8s

Calls
45 calls:
Slowest
741.0ms
(* (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
342.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
341.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
275.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
248.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes249.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.6s2948×body1280valid
1.6s1840×body640valid
476.0ms782×body320valid
361.0ms2096×body80valid
162.0ms336×body160valid