Details

Time bar (total: 27.7s)

sample210.0ms

Algorithm
intervals
Results
101.0ms84×body1280valid
33.0ms61×body640valid
10.0ms72×body80valid
8.0ms20×body320valid
5.0ms19×body160valid

simplify66.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
65.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize18.0ms

Local error

Found 3 expressions with local error:

2.6b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite41.0ms

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
18.0ms
(* r (sin b))
11.0ms
(/ (* r (sin b)) (cos (+ a b)))
9.0ms
(cos (+ a b))

series250.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
155.0ms
(/ (* r (sin b)) (cos (+ a b)))
53.0ms
(* r (sin b))
41.0ms
(cos (+ a b))

simplify1.5s

Counts
33 → 59
Calls
33 calls:
Slowest
290.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
219.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
218.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
175.0ms
(- (+ (log r) (log (sin b))) (log (cos (+ a b))))
158.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune685.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

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

rewrite73.0ms

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
29.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms
(* (sin a) (sin b))
7.0ms
(* r (sin b))

series560.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
309.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
116.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms
(* (sin a) (sin b))
65.0ms
(* r (sin b))

simplify3.5s

Counts
53 → 92
Calls
53 calls:
Slowest
334.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
302.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
300.0ms
(/ (* (* (* 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)))))
293.0ms
(/ (* (* (* 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)))))
286.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

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
51.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
24.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
21.0ms
(* (sin a) (sin b))
16.0ms
(* (sin b) r)

series550.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
350.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
99.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
52.0ms
(* (sin b) r)
50.0ms
(* (sin a) (sin b))

simplify3.7s

Counts
53 → 92
Calls
53 calls:
Slowest
351.0ms
(/ (* (* (* (sin b) (sin b)) (sin b)) (* (* r r) r)) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
344.0ms
(/ (* (* (* (sin b) r) (* (sin b) r)) (* (sin b) r)) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
325.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
319.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
282.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* r r) r))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

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))

rewrite85.0ms

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
31.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
23.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
14.0ms
(* (/ (cos b) (sin b)) (cos a))
13.0ms
(/ (cos b) (sin b))

series500.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
290.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
121.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
66.0ms
(* (/ (cos b) (sin b)) (cos a))
23.0ms
(/ (cos b) (sin b))

simplify4.0s

Counts
90 → 116
Calls
90 calls:
Slowest
407.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
304.0ms
(/ (* (* 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))))
285.0ms
(- (/ 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))))
238.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes277.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.3s2853×body1280valid
1.9s1834×body640valid
511.0ms2159×body80valid
420.0ms790×body320valid
154.0ms365×body160valid