Details

Time bar (total: 44.6s)

sample775.0ms

Algorithm
intervals
Results
491.0ms25×body320valid
91.0ms92×body1280valid
45.0ms62×body640valid
9.0ms64×body80valid
4.0ms13×body160valid

simplify69.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
68.0ms
(* r (/ (sin b) (cos (+ a b))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize58.0ms

Local error

Found 3 expressions with local error:

2.5b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite61.0ms

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
25.0ms
(* r (/ (sin b) (cos (+ a b))))
17.0ms
(cos (+ a b))
16.0ms
(/ (sin b) (cos (+ a b)))

series220.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
129.0ms
(* r (/ (sin b) (cos (+ a b))))
55.0ms
(/ (sin b) (cos (+ a b)))
35.0ms
(cos (+ a b))

simplify2.3s

Counts
60 → 79
Calls
60 calls:
Slowest
403.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
303.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
255.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
230.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
154.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune827.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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)) (* (sin a) (sin b)))

rewrite208.0ms

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/
Counts
4 → 104
Calls
4 calls:
Slowest
104.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
47.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
34.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
21.0ms
(* (sin a) (sin b))

series714.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
311.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
178.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
137.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
88.0ms
(* (sin a) (sin b))

simplify5.2s

Counts
83 → 116
Calls
83 calls:
Slowest
386.0ms
(* (* (* 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))))))
316.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
315.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
283.0ms
(/ (* (* (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)))))
280.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

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
(* r (sin b))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
27×add-sqr-sqrt
23×*-un-lft-identity associate-*r* add-cube-cbrt
22×add-cbrt-cube
18×times-frac
14×pow1 prod-exp
8×associate-/r/ cbrt-unprod
7×associate-*l*
6×div-exp
5×pow-prod-down sin-mult
4×cos-mult insert-posit16 add-log-exp
3×cbrt-undiv rec-exp associate-/r* 1-exp *-commutative associate-/l*
2×flip3-- frac-sub div-inv flip-- sub-div unswap-sqr
1×clear-num frac-2neg associate-*r/ un-div-inv pow-flip inv-pow
Counts
4 → 118
Calls
4 calls:
Slowest
118.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
50.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))
9.0ms
(* r (sin b))

series565.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
319.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
145.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
60.0ms
(* (sin a) (sin b))
40.0ms
(* r (sin b))

simplify6.1s

Counts
95 → 130
Calls
95 calls:
Slowest
359.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
331.0ms
(* (* (* (* r (sin b)) (* r (sin b))) (* r (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))))))
289.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
281.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
267.0ms
(* (* (* (* 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))))))

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
58×add-sqr-sqrt
56×*-un-lft-identity add-cube-cbrt
16×associate-/r*
13×add-cbrt-cube add-exp-log
6×pow1 div-inv associate-/l* add-log-exp
5×sin-mult
4×cbrt-undiv div-exp cos-mult insert-posit16 associate-/l/
3×associate-*r* associate-*l*
2×clear-num frac-2neg flip3-- frac-sub flip-- sub-div
1×sub-neg diff-log div-sub pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod unswap-sqr
Counts
4 → 139
Calls
4 calls:
Slowest
24.0ms
(/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r)
20.0ms
(* (sin b) (sin a))
18.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
16.0ms
(/ (sin b) (/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r))

series766.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
416.0ms
(/ (sin b) (/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r))
167.0ms
(/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r)
123.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
61.0ms
(* (sin b) (sin a))

simplify13.5s

Counts
153 → 151
Calls
153 calls:
Slowest
418.0ms
(/ (* (* (- (* (cos b) (cos a)) (* (sin b) (sin a))) (- (* (cos b) (cos a)) (* (sin b) (sin a)))) (- (* (cos b) (cos a)) (* (sin b) (sin a)))) (* (* r r) r))
416.0ms
(- (pow (* (cos b) (cos a)) 3) (pow (* (sin b) (sin a)) 3))
357.0ms
(- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin b) (sin a)) (* (sin b) (sin a))))
312.0ms
(- (+ (cos (+ b a)) (cos (- b a))) (- (cos (- b a)) (cos (+ b a))))
310.0ms
(- (+ (cos (+ b a)) (cos (- b a))) (- (cos (- b a)) (cos (+ b a))))

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes330.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
4.1s2836×body1280valid
1.6s1887×body640valid
432.0ms2162×body80valid
413.0ms784×body320valid
174.0ms333×body160valid