Details

Time bar (total: 40.3s)

sample255.0ms

Algorithm
intervals
Results
83.0ms103×body1280valid
48.0ms22×body320valid
31.0ms59×body640valid
10.0ms64×body80valid
2.0ms8×body160valid

simplify90.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
90.0ms
(* r (/ (sin b) (cos (+ a b))))

prune89.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize81.0ms

Local error

Found 3 expressions with local error:

2.2b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite63.0ms

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
26.0ms
(* r (/ (sin b) (cos (+ a b))))
20.0ms
(cos (+ a b))
12.0ms
(/ (sin b) (cos (+ a b)))

series265.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
139.0ms
(* r (/ (sin b) (cos (+ a b))))
68.0ms
(/ (sin b) (cos (+ a b)))
57.0ms
(cos (+ a b))

simplify2.4s

Counts
60 → 79
Calls
60 calls:
Slowest
438.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
287.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
245.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
199.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
185.0ms
(* (* (* r r) r) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b)))))

prune838.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (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))

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
87.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
15.0ms
(* (cos a) (cos b))
14.0ms
(* (sin a) (sin b))

series622.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
350.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
143.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
69.0ms
(* (sin a) (sin b))
60.0ms
(* (cos a) (cos b))

simplify5.0s

Counts
90 → 121
Calls
90 calls:
Slowest
376.0ms
(* (* (* 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))))))
367.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
342.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
341.0ms
(/ (* (* (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)))))
324.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

23.5b
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))

rewrite778.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
29×sin-mult
20×add-cbrt-cube add-exp-log
18×pow-prod-down
16×add-sqr-sqrt
14×cbrt-div *-un-lft-identity add-cube-cbrt
11×frac-times associate-*l/
9×times-frac prod-exp associate-/r/ cbrt-unprod
7×associate-*r/ cos-mult frac-sub
4×associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16 add-log-exp
3×associate-/r* associate-/l*
2×pow-plus *-commutative
1×cbrt-prod pow2 cbrt-undiv clear-num frac-2neg flip3-- pow1/3 swap-sqr div-exp pow3 rem-cbrt-cube div-inv flip-- unswap-sqr
Counts
4 → 113
Calls
4 calls:
Slowest
534.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
136.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
83.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
22.0ms
(* (sin a) (sin b))

series389.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
82.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
63.0ms
(* (sin a) (sin b))
58.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

simplify12.3s

Counts
103 → 125
Calls
103 calls:
Slowest
848.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
826.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
411.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
411.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))))
369.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))))

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

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
42.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms
(* (sin a) (sin b))
16.0ms
(* (cos a) (cos b))
14.0ms
(* r (sin b))

series466.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
294.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
61.0ms
(* (sin a) (sin b))
60.0ms
(* (cos a) (cos b))
50.0ms
(* r (sin b))

simplify3.3s

Counts
60 → 97
Calls
60 calls:
Slowest
350.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
319.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
306.0ms
(/ (* (* (* 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)))))
291.0ms
(/ (* (* (* r r) r) (* (* (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)))))
286.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes244.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.3s2972×body1280valid
1.5s1821×body640valid
827.0ms726×body320valid
370.0ms2118×body80valid
165.0ms364×body160valid