Details

Time bar (total: 36.6s)

sample1.2s

Algorithm
intervals
Results
189.0ms98×body1280valid
65.0ms62×body640valid
14.0ms69×body80valid
12.0ms18×body320valid
4.0ms9×body160valid

simplify51.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize60.0ms

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))))

rewrite33.0ms

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
12.0ms
(* r (/ (sin b) (cos (+ a b))))
11.0ms
(cos (+ a b))
8.0ms
(/ (sin b) (cos (+ a b)))

series200.0ms

Calls
3 calls:
Slowest
125.0ms
(* r (/ (sin b) (cos (+ a b))))
42.0ms
(/ (sin b) (cos (+ a b)))
32.0ms
(cos (+ a b))

simplify2.5s

Calls
60 calls:
Slowest
491.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
307.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
259.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
206.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
181.0ms
(* (* (* r r) r) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b)))))

prune884.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

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)))

rewrite165.0ms

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
79.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
53.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(* (sin a) (sin b))
15.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))

series612.0ms

Calls
4 calls:
Slowest
273.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
180.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
103.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
57.0ms
(* (sin a) (sin b))

simplify5.5s

Calls
83 calls:
Slowest
383.0ms
(* (* (* 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))))))
378.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
310.0ms
(/ (* (* (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)))))
300.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
293.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize40.0ms

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))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity times-frac add-cube-cbrt
13×add-cbrt-cube associate-*l* add-exp-log
6×pow1 associate-/r* associate-/l* add-log-exp
4×insert-posit16
3×cbrt-undiv div-exp associate-*r* div-inv
2×clear-num frac-2neg flip3-- prod-exp associate-/r/ cbrt-unprod flip-- unswap-sqr
1×sub-neg diff-log pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
24.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
19.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
15.0ms
(* (/ (cos b) (sin b)) (cos a))
8.0ms
(/ (cos b) (sin b))

series535.0ms

Calls
4 calls:
Slowest
241.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
155.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
101.0ms
(* (/ (cos b) (sin b)) (cos a))
37.0ms
(/ (cos b) (sin b))

simplify4.3s

Calls
90 calls:
Slowest
386.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
324.0ms
(/ (* (* r r) r) (* (* (- (* (/ (cos b) (sin b)) (cos a)) (sin a)) (- (* (/ (cos b) (sin b)) (cos a)) (sin a))) (- (* (/ (cos b) (sin b)) (cos a)) (sin a))))
320.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))
318.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
278.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize57.0ms

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)))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube associate-*r*
18×times-frac
13×prod-exp
12×pow1
8×associate-/r/
7×cbrt-unprod sin-mult
6×div-exp cos-mult add-log-exp
4×associate-*l* pow-prod-down insert-posit16
3×cbrt-undiv rec-exp associate-/r* flip3-- 1-exp frac-sub flip-- associate-/l* sub-div
2×*-commutative div-inv
1×clear-num sub-neg frac-2neg diff-log associate-*r/ un-div-inv pow-flip inv-pow unswap-sqr
Calls
4 calls:
Slowest
100.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
57.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))
15.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))

series704.0ms

Calls
4 calls:
Slowest
325.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
159.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
133.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
87.0ms
(* (sin a) (sin b))

simplify7.2s

Calls
89 calls:
Slowest
357.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
357.0ms
(* (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (/ (* (* 1 1) 1) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
332.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
319.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
309.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes286.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.1s

Algorithm
intervals
Results
3.6s2948×body1280valid
2.2s1840×body640valid
466.0ms782×body320valid
422.0ms2096×body80valid
139.0ms336×body160valid