Details

Time bar (total: 35.0s)

sample399.0ms

Algorithm
intervals
Results
158.0ms88×body1280valid
56.0ms64×body640valid
19.0ms72×body80valid
15.0ms22×body320valid
4.0ms10×body160valid

simplify52.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
51.0ms
(* r (/ (sin b) (cos (+ a b))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize34.0ms

Local error

Found 3 expressions with local error:

4.4b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite67.0ms

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
35.0ms
(cos (+ a b))
18.0ms
(/ (sin b) (cos (+ a b)))
12.0ms
(* r (/ (sin b) (cos (+ a b))))

series216.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
121.0ms
(* r (/ (sin b) (cos (+ a b))))
63.0ms
(/ (sin b) (cos (+ a b)))
31.0ms
(cos (+ a b))

simplify2.3s

Counts
60 → 79
Calls
60 calls:
Slowest
430.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
293.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
260.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
192.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
173.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune963.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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)) (* (sin a) (sin b)))

rewrite181.0ms

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
97.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
44.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms
(* (sin a) (sin b))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))

series732.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
343.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
177.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
144.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
68.0ms
(* (sin a) (sin b))

simplify5.7s

Counts
83 → 116
Calls
83 calls:
Slowest
373.0ms
(* (* (* 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))))))
345.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
334.0ms
(/ (* (* (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)))))
330.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
312.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 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))))
0.2b
(* r (sin b))

rewrite164.0ms

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
73.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
60.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
15.0ms
(* (sin a) (sin b))
14.0ms
(* r (sin b))

series538.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
298.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
120.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
61.0ms
(* (sin a) (sin b))
58.0ms
(* r (sin b))

simplify6.5s

Counts
95 → 130
Calls
95 calls:
Slowest
309.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
309.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
299.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (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)))))
286.0ms
(* (* (* (* 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))))))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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

rewrite122.0ms

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
46.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
29.0ms
(* (/ (cos b) (sin b)) (cos a))
28.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
18.0ms
(/ (cos b) (sin b))

series549.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
278.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
143.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
90.0ms
(* (/ (cos b) (sin b)) (cos a))
38.0ms
(/ (cos b) (sin b))

simplify4.2s

Counts
90 → 116
Calls
90 calls:
Slowest
406.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
309.0ms
(/ (* (* 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))))
294.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))
283.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
245.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes245.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.1s

Algorithm
intervals
Results
3.6s2947×body1280valid
2.0s1798×body640valid
849.0ms745×body320valid
355.0ms2151×body80valid
126.0ms362×body160valid