Details

Time bar (total: 25.2s)

sample244.0ms

Algorithm
intervals
Results
84.0ms89×body1280valid
52.0ms26×body320valid
36.0ms63×body640valid
8.0ms67×body80valid
3.0ms11×body160valid

simplify231.0ms

Calls
1 calls:
Slowest
231.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize31.0ms

Local error

Found 3 expressions with local error:

2.9b
(cos (+ a b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×add-cbrt-cube add-exp-log
3×pow1 associate-/r* times-frac associate-*r* insert-posit16 add-log-exp
1×cbrt-undiv cos-sum clear-num frac-2neg div-exp *-commutative div-inv associate-/l*
Calls
3 calls:
Slowest
10.0ms
(/ (* r (sin b)) (cos (+ a b)))
6.0ms
(cos (+ a b))
2.0ms
(* r (sin b))

series165.0ms

Calls
3 calls:
Slowest
105.0ms
(/ (* r (sin b)) (cos (+ a b)))
34.0ms
(* r (sin b))
25.0ms
(cos (+ a b))

simplify769.0ms

Calls
24 calls:
Slowest
289.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
151.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
135.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
47.0ms
(- (log (* r (sin b))) (log (cos (+ a b))))
37.0ms
(/ (* (sin b) r) (cos (+ a b)))

prune574.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 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)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×pow1 associate-*r* add-log-exp
5×sin-mult
4×associate-/r/ cos-mult insert-posit16
3×associate-/r* times-frac associate-*l*
2×flip3-- *-commutative frac-sub flip-- sub-div
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp pow-prod-down prod-exp cbrt-unprod div-inv associate-/l*
Calls
4 calls:
Slowest
25.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms
(* (sin a) (sin b))
3.0ms
(* r (sin b))

series409.0ms

Calls
4 calls:
Slowest
224.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
82.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
56.0ms
(* (sin a) (sin b))
47.0ms
(* r (sin b))

simplify2.6s

Calls
42 calls:
Slowest
296.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
286.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
282.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
263.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
234.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (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)))))

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

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)))

rewrite46.0ms

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
18.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms
(* (sin a) (sin b))

series557.0ms

Calls
4 calls:
Slowest
238.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
139.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
115.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
65.0ms
(* (sin a) (sin b))

simplify3.8s

Calls
70 calls:
Slowest
376.0ms
(/ (* (* (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)))))
322.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
312.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
256.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
218.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

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
17.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
13.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
13.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
4.0ms
(* (sin b) (sin a))

series528.0ms

Calls
4 calls:
Slowest
241.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
140.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
92.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
54.0ms
(* (sin b) (sin a))

simplify3.6s

Calls
70 calls:
Slowest
378.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- b a)) (cos (+ b a)))))
297.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (* (sin b) (sin a))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
242.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
227.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- b a)) (cos (+ b a))))
199.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos a) (cos b)) (* (sin b) (sin a)))))

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes380.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
4.4s2864×body1280valid
1.6s1846×body640valid
496.0ms743×body320valid
400.0ms2172×body80valid
127.0ms376×body160valid