Details

Time bar (total: 3.0m)

sample252.0ms

Algorithm
intervals
Results
80.0ms79×body1280valid
49.0ms79×body80valid
46.0ms62×body640valid
11.0ms25×body320valid
5.0ms11×body160valid

simplify39.0ms

Calls
1 calls:
Slowest
39.0ms
(* r (/ (sin b) (cos (+ a b))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize36.0ms

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))))

rewrite35.0ms

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×associate-/r* associate-*l* insert-posit16 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
14.0ms
(* r (/ (sin b) (cos (+ a b))))
9.0ms
(/ (sin b) (cos (+ a b)))
9.0ms
(cos (+ a b))

series268.0ms

Calls
3 calls:
Slowest
164.0ms
(* r (/ (sin b) (cos (+ a b))))
64.0ms
(/ (sin b) (cos (+ a b)))
41.0ms
(cos (+ a b))

simplify2.5s

Calls
60 calls:
Slowest
421.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
357.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
234.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
231.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
208.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune941.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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)))

rewrite134.0ms

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×insert-posit16
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 diff-log associate-*r/
Calls
4 calls:
Slowest
68.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
33.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms
(* (sin a) (sin b))

series650.0ms

Calls
4 calls:
Slowest
293.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
146.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
129.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
81.0ms
(* (sin a) (sin b))

simplify6.1s

Calls
83 calls:
Slowest
562.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
399.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
381.0ms
(* (* (* 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))))))
339.0ms
(/ (* (* (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)))))
304.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite338.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
82×pow1
65×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
35×add-cbrt-cube add-exp-log
34×pow-prod-down
27×cos-mult sin-mult
22×associate-/r*
16×prod-exp associate-/r/ cbrt-unprod difference-of-squares associate-/l/
12×associate-*l/ associate-*r/
10×frac-times
9×frac-sub
8×pow-sqr pow-prod-up
7×associate-/l*
6×div-inv
5×flip3-+ frac-add flip-+ sub-div
4×cbrt-undiv pow-plus div-exp insert-posit16 add-log-exp
2×pow2 clear-num frac-2neg swap-sqr associate-*r* associate-*l* *-commutative
1×flip3-- div-sub flip--
Calls
4 calls:
Slowest
163.0ms
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
64.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
60.0ms
(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

series798.0ms

Calls
4 calls:
Slowest
367.0ms
(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
289.0ms
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
71.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
70.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify49.7s

Calls
278 calls:
Slowest
1.1s
(/ (* (* (sin b) (sin b)) (sin b)) (/ (* (* (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (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))))))
833.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
787.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
672.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
665.0ms
(* (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))))

prune3.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
229×add-sqr-sqrt
223×*-un-lft-identity add-cube-cbrt
56×associate-/r*
53×associate-/r/
27×sin-mult
24×cos-mult
19×add-cbrt-cube add-exp-log
17×div-inv
12×flip3-- frac-sub flip-- sub-div
10×pow1
9×associate-*r* associate-*l*
6×cbrt-undiv div-exp
4×insert-posit16 add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod associate-/l* unswap-sqr
1×clear-num frac-2neg
Calls
4 calls:
Slowest
79.0ms
(/ (sin b) (/ (+ (* (sin b) (sin a)) (* (cos b) (cos a))) (/ (+ (* (sin b) (sin a)) (* (cos b) (cos a))) (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
21.0ms
(* (sin b) (sin a))
14.0ms
(* (sin b) (sin a))
14.0ms
(* (sin b) (sin a))

series365.0ms

Calls
4 calls:
Slowest
155.0ms
(/ (sin b) (/ (+ (* (sin b) (sin a)) (* (cos b) (cos a))) (/ (+ (* (sin b) (sin a)) (* (cos b) (cos a))) (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
80.0ms
(* (sin b) (sin a))
67.0ms
(* (sin b) (sin a))
63.0ms
(* (sin b) (sin a))

simplify1.6m

Calls
446 calls:
Slowest
1.7s
(/ (sqrt (sin b)) (/ (* (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a)))) (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a))))) (/ (* (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a)))) (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a))))) 1)))
1.2s
(/ (sqrt (sin b)) (/ (* (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a)))) (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a))))) (/ (* (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a)))) (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a))))) (sqrt (- (* (cos b) (cos a)) (* (sin b) (sin a)))))))
902.0ms
(/ (sin b) (/ (+ (* (sin b) (sin a)) (* (cos b) (cos a))) (/ (+ (* (sin b) (sin a)) (* (cos b) (cos a))) (sqrt (- (* (cos b) (cos a)) (* (sin b) (sin a)))))))
871.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (/ (* (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a)))) (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a))))) (/ (* (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a)))) (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a))))) (* (cbrt (- (* (cos b) (cos a)) (* (sin b) (sin a)))) (cbrt (- (* (cos b) (cos a)) (* (sin b) (sin a))))))))
862.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (/ (sqrt (+ (* (sin b) (sin a)) (* (cos b) (cos a)))) (/ (sqrt (+ (* (sin b) (sin a)) (* (cos b) (cos a)))) (sqrt (- (* (cos b) (cos a)) (* (sin b) (sin a)))))))

prune5.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes370.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.5s2880×body1280valid
1.6s1861×body640valid
439.0ms752×body320valid
415.0ms2131×body80valid
130.0ms378×body160valid