Details

Time bar (total: 30.2s)

sample460.0ms

Algorithm
intervals
Results
122.0ms87×body1280valid
118.0ms70×body640valid
15.0ms23×body320valid
14.0ms63×body80valid
5.0ms13×body160valid

simplify36.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
35.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize33.0ms

Local error

Found 3 expressions with local error:

3.2b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite31.0ms

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
12.0ms
(/ (* r (sin b)) (cos (+ a b)))
9.0ms
(cos (+ a b))
8.0ms
(* r (sin b))

series181.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
105.0ms
(/ (* r (sin b)) (cos (+ a b)))
46.0ms
(* r (sin b))
29.0ms
(cos (+ a b))

simplify1.4s

Counts
33 → 59
Calls
33 calls:
Slowest
315.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
227.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
226.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
209.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
183.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune701.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

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)) (* (sin a) (sin b)))
0.1b
(* r (sin b))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×associate-/r/ cos-mult insert-posit16
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×clear-num sub-neg frac-2neg diff-log div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
Slowest
53.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))
16.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms
(* r (sin b))

series619.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
313.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
152.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
81.0ms
(* (sin a) (sin b))
74.0ms
(* r (sin b))

simplify3.5s

Counts
53 → 92
Calls
53 calls:
Slowest
344.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
333.0ms
(/ (* (* (* 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)))))
292.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
284.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
274.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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

rewrite86.0ms

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
Counts
4 → 104
Calls
4 calls:
Slowest
39.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
23.0ms
(* (/ (cos b) (sin b)) (cos a))
13.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
8.0ms
(/ (cos b) (sin b))

series516.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
279.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
111.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
93.0ms
(* (/ (cos b) (sin b)) (cos a))
33.0ms
(/ (cos b) (sin b))

simplify4.2s

Counts
90 → 116
Calls
90 calls:
Slowest
476.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
355.0ms
(/ (* (* 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))))
316.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
270.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))
265.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

3.0b
(log (exp (* (sin a) (sin b))))
0.2b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))
0.1b
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
7×pow1
6×log-prod add-log-exp
4×insert-posit16
3×associate-/r* times-frac associate-*r* associate-*l* log-pow associate--r+
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod flip--
1×exp-prod clear-num sub-neg frac-2neg exp-to-pow diff-log rem-log-exp pow-prod-down *-commutative div-inv sin-mult associate-/l* unswap-sqr
Counts
4 → 75
Calls
4 calls:
Slowest
27.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
22.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
10.0ms
(* (sin a) (sin b))
5.0ms
(log (exp (* (sin a) (sin b))))

series572.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
314.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
136.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
62.0ms
(log (exp (* (sin a) (sin b))))
59.0ms
(* (sin a) (sin b))

simplify5.3s

Counts
48 → 87
Calls
48 calls:
Slowest
577.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
360.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
340.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
304.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
283.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes363.0ms

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
4.6s2921×body1280valid
1.5s1775×body640valid
538.0ms796×body320valid
460.0ms2156×body80valid
224.0ms353×body160valid