Details

Time bar (total: 1.4m)

sample294.0ms

Algorithm
intervals
Results
94.0ms84×body1280valid
61.0ms70×body80valid
46.0ms61×body640valid
15.0ms25×body320valid
6.0ms16×body160valid

simplify79.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
78.0ms
(* r (/ (sin b) (cos (+ a b))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize27.0ms

Local error

Found 3 expressions with local error:

3.2b
(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
Counts
3 → 70
Calls
3 calls:
Slowest
14.0ms
(* r (/ (sin b) (cos (+ a b))))
9.0ms
(/ (sin b) (cos (+ a b)))
9.0ms
(cos (+ a b))

series224.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
134.0ms
(* r (/ (sin b) (cos (+ a b))))
52.0ms
(/ (sin b) (cos (+ a b)))
38.0ms
(cos (+ a b))

simplify2.3s

Counts
60 → 79
Calls
60 calls:
Slowest
456.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
320.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
246.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
209.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
127.0ms
(* (* (* r r) r) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b)))))

prune847.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

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

rewrite170.0ms

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/
Counts
4 → 104
Calls
4 calls:
Slowest
100.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
30.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms
(* (sin a) (sin b))
16.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))

series592.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
272.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
151.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
111.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
58.0ms
(* (sin a) (sin b))

simplify5.6s

Counts
83 → 116
Calls
83 calls:
Slowest
452.0ms
(* (* (* 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))))))
380.0ms
(/ (* (* (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)))))
337.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
322.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
307.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (* (cos a) (cos b)) 3)
0.3b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b
(pow (* (sin a) (sin b)) 3)
0.3b
(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
69×cos-mult
60×frac-add
57×sin-mult
49×pow1
36×add-sqr-sqrt
35×associate-/r/
30×frac-times associate-*l/ associate-*r/
28×*-un-lft-identity
27×times-frac
24×add-cbrt-cube add-exp-log
20×add-cube-cbrt
19×pow-prod-down
18×sqr-pow
16×difference-of-squares
10×prod-exp cbrt-unprod
9×associate-/l*
6×cube-div pow-unpow
4×difference-cubes pow-pow flip3-+ pow-exp pow-sqr pow-prod-up flip-+ insert-posit16 distribute-lft-out-- add-log-exp rem-cube-cbrt associate-/l/
3×associate-/r*
2×cube-mult pow-to-exp unpow-prod-down pow-plus unpow3 cube-prod
1×pow2 cbrt-undiv clear-num frac-2neg flip3-- div-sub swap-sqr div-exp associate-*r* associate-*l* *-commutative frac-sub div-inv flip-- sub-div
Counts
4 → 178
Calls
4 calls:
Slowest
269.0ms
(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))))
48.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
9.0ms
(pow (* (sin a) (sin b)) 3)
7.0ms
(pow (* (cos a) (cos b)) 3)

series714.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
468.0ms
(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))))
93.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
79.0ms
(pow (* (cos a) (cos b)) 3)
73.0ms
(pow (* (sin a) (sin b)) 3)

simplify29.1s

Counts
177 → 190
Calls
177 calls:
Slowest
940.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
751.0ms
(+ (* (* (* (cos a) (cos b)) (* (cos a) (cos 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)))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos 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)))))))
670.0ms
(/ (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))) (sqrt (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))))
609.0ms
(* 2 (+ (* (* (* (sin a) (sin b)) (* (sin a) (sin 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)))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))))
605.0ms
(* (* 2 2) (+ (* (* (* (sin a) (sin b)) (* (sin a) (sin 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)))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))))

prune3.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
121×pow1
71×associate-*r/
60×cos-mult
51×pow-prod-down
42×add-cbrt-cube add-exp-log
40×sin-mult
37×associate-*l/
27×frac-times frac-add
24×prod-exp cbrt-unprod
23×associate-/r/
16×associate-/l/
12×add-sqr-sqrt *-un-lft-identity pow-sqr pow-prod-up add-cube-cbrt
9×times-frac frac-sub
7×flip3-+ flip-+
6×pow-plus
5×sub-div
4×insert-posit16 add-log-exp
3×pow2 associate-/r* swap-sqr associate-*r* associate-*l* *-commutative associate-/l*
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp div-inv flip--
Counts
4 → 182
Calls
4 calls:
Slowest
1.2s
(/ (- (* (cos a) (* (cos b) (* (* (cos b) (cos a)) (* (cos b) (cos a))))) (* (* (sin a) (* (* (sin b) (sin a)) (* (sin b) (sin a)))) (sin b))) (+ (* (* (sin b) (sin a)) (+ (* (cos b) (cos a)) (* (sin b) (sin a)))) (* (* (cos b) (cos a)) (* (cos b) (cos a)))))
52.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
49.0ms
(* (* (cos b) (cos a)) (* (cos b) (cos a)))
35.0ms
(* (* (cos b) (cos a)) (* (cos b) (cos a)))

series706.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
498.0ms
(/ (- (* (cos a) (* (cos b) (* (* (cos b) (cos a)) (* (cos b) (cos a))))) (* (* (sin a) (* (* (sin b) (sin a)) (* (sin b) (sin a)))) (sin b))) (+ (* (* (sin b) (sin a)) (+ (* (cos b) (cos a)) (* (sin b) (sin a)))) (* (* (cos b) (cos a)) (* (cos b) (cos a)))))
73.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
71.0ms
(* (* (cos b) (cos a)) (* (cos b) (cos a)))
64.0ms
(* (* (cos b) (cos a)) (* (cos b) (cos a)))

simplify24.5s

Counts
188 → 194
Calls
188 calls:
Slowest
891.0ms
(/ (* (* (- (* (cos a) (* (cos b) (* (* (cos b) (cos a)) (* (cos b) (cos a))))) (* (* (sin a) (* (* (sin b) (sin a)) (* (sin b) (sin a)))) (sin b))) (- (* (cos a) (* (cos b) (* (* (cos b) (cos a)) (* (cos b) (cos a))))) (* (* (sin a) (* (* (sin b) (sin a)) (* (sin b) (sin a)))) (sin b)))) (- (* (cos a) (* (cos b) (* (* (cos b) (cos a)) (* (cos b) (cos a))))) (* (* (sin a) (* (* (sin b) (sin a)) (* (sin b) (sin a)))) (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)) (+ (* (cos b) (cos a)) (* (sin b) (sin a)))) (* (* (cos b) (cos a)) (* (cos b) (cos a))))) (+ (* (* (sin b) (sin a)) (+ (* (cos b) (cos a)) (* (sin b) (sin a)))) (* (* (cos b) (cos a)) (* (cos b) (cos a))))))
861.0ms
(* (* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a))) (* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a))))
835.0ms
(* (* (* (* (cos b) (cos b)) (cos b)) (* (* (cos a) (cos a)) (cos a))) (* (* (* (cos b) (cos b)) (cos b)) (* (* (cos a) (cos a)) (cos a))))
717.0ms
(* (* (* (* (cos b) (cos b)) (cos b)) (* (* (cos a) (cos a)) (cos a))) (* (* (* (cos b) (cos b)) (cos b)) (* (* (cos a) (cos a)) (cos a))))
713.0ms
(* (* (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (cos b) (cos a))) (* (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (cos b) (cos a))))

prune4.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes336.0ms

Accuracy

0% (0.4b remaining)

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

bsearch13.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
3.7s2939×body1280valid
2.0s1846×body640valid
787.0ms2103×body80valid
463.0ms755×body320valid
168.0ms358×body160valid