Details

Time bar (total: 53.9s)

sample376.0ms

Algorithm
intervals
Results
147.0ms68×body640valid
79.0ms83×body1280valid
9.0ms21×body320valid
8.0ms67×body80valid
5.0ms17×body160valid

simplify88.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
86.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize38.0ms

Local error

Found 3 expressions with local error:

3.5b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1
3×associate-/r* times-frac associate-*r* associate-*l* insert-posit16 add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×cos-sum clear-num frac-2neg pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 50
Calls
3 calls:
Slowest
35.0ms
(cos (+ a b))
25.0ms
(/ (* r (sin b)) (cos (+ a b)))
15.0ms
(* r (sin b))

series251.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
154.0ms
(/ (* r (sin b)) (cos (+ a b)))
56.0ms
(* r (sin b))
41.0ms
(cos (+ a b))

simplify3.2s

Counts
64 → 59
Calls
64 calls:
Slowest
404.0ms
(/ (* (sin b) r) (cos (+ a b)))
395.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
290.0ms
(* (* (/ (* r (sin b)) (cos (+ a b))) (/ (* r (sin b)) (cos (+ a b)))) (/ (* r (sin b)) (cos (+ a b))))
258.0ms
(* (* (* r (sin b)) (* r (sin b))) (* r (sin b)))
227.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune578.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-cbrt-cube add-exp-log
12×*-un-lft-identity add-cube-cbrt
10×pow1
9×associate-*r* associate-*l*
4×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp
3×associate-/r* times-frac pow-prod-down cos-mult *-commutative sin-mult unswap-sqr
2×cbrt-undiv div-exp
1×clear-num frac-2neg flip3-- frac-sub div-inv flip-- associate-/l* sub-div
Counts
4 → 85
Calls
4 calls:
Slowest
57.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms
(* (sin a) (sin b))
9.0ms
(* (cos a) (cos b))
8.0ms
(* r (sin b))

series506.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
299.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
76.0ms
(* (sin a) (sin b))
73.0ms
(* (cos a) (cos b))
57.0ms
(* r (sin b))

simplify7.4s

Counts
101 → 97
Calls
101 calls:
Slowest
446.0ms
(/ (* r (sin b)) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))
411.0ms
(* (* (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
393.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
390.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b)))
341.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* (sin a) (sin b))
0.1b
(* (cos a) (cos b))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
23×associate-*r*
19×times-frac
15×add-cbrt-cube add-exp-log
10×pow1
9×associate-*l*
8×associate-/r/
5×cos-mult sin-mult
4×prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×associate-/r* pow-prod-down *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp frac-sub div-inv flip-- sub-div
1×clear-num frac-2neg associate-*r/
Counts
4 → 109
Calls
4 calls:
Slowest
109.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms
(* (sin a) (sin b))
9.0ms
(* (cos a) (cos b))

series648.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
175.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
77.0ms
(* (sin a) (sin b))
68.0ms
(* (cos a) (cos b))

simplify10.9s

Counts
132 → 121
Calls
132 calls:
Slowest
471.0ms
(/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)))
405.0ms
(/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b))))))
400.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
400.0ms
(* r (/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))))
385.0ms
(* (* (* 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))))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
160×pow1
68×pow-prod-down
52×add-cbrt-cube add-exp-log
32×prod-exp cbrt-unprod
16×pow-sqr pow-prod-up
8×pow-plus cos-mult sin-mult
4×pow2 add-sqr-sqrt frac-times *-un-lft-identity swap-sqr associate-*r* associate-*l* associate-*l/ associate-*r/ *-commutative add-cube-cbrt insert-posit16 add-log-exp
Counts
4 → 152
Calls
4 calls:
Slowest
83.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
51.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
42.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
36.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
95.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
91.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
76.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
70.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

simplify15.5s

Counts
164 → 164
Calls
164 calls:
Slowest
1.3s
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
813.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
812.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
786.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
756.0ms
(* (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))))

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes252.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.5s2957×body1280valid
1.5s1852×body640valid
452.0ms739×body320valid
418.0ms2117×body80valid
159.0ms338×body160valid