Details

Time bar (total: 1.5m)

sample329.0ms

Algorithm
intervals
Results
114.0ms98×body1280valid
87.0ms51×body640valid
13.0ms75×body80valid
9.0ms14×body320valid
7.0ms18×body160valid

simplify33.0ms

Calls
1 calls:
Slowest
32.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize53.0ms

Local error

Found 3 expressions with local error:

3.3b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
36×times-frac
30×*-un-lft-identity add-cube-cbrt
15×associate-*r* associate-*l*
12×associate-/l*
10×add-cbrt-cube add-exp-log
5×pow1 *-commutative unswap-sqr
3×associate-/r* insert-posit16 add-log-exp
2×cbrt-undiv cos-sum div-exp prod-exp cbrt-unprod
1×+-commutative clear-num frac-2neg pow-prod-down div-inv
Calls
3 calls:
Slowest
16.0ms
(/ (* r (sin b)) (cos (+ a b)))
10.0ms
(cos (+ a b))
8.0ms
(* r (sin b))

series217.0ms

Calls
3 calls:
Slowest
144.0ms
(/ (* r (sin b)) (cos (+ a b)))
46.0ms
(* r (sin b))
25.0ms
(cos (+ a b))

simplify3.4s

Calls
109 calls:
Slowest
335.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
225.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
217.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
186.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
167.0ms
(/ (* r (* (cbrt (sin b)) (cbrt (sin b)))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
253×add-sqr-sqrt
169×*-un-lft-identity
132×times-frac
98×associate-*l*
70×unswap-sqr
57×add-cube-cbrt
56×distribute-lft-out-- difference-of-squares
42×associate-*r*
14×*-commutative
13×add-cbrt-cube add-exp-log
12×associate-/l*
11×associate-/r*
8×pow1
6×add-log-exp
5×sin-mult
4×associate-/r/ cos-mult insert-posit16
3×prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down frac-sub flip-- sub-div
1×clear-num sub-neg frac-2neg diff-log div-inv
Calls
4 calls:
Slowest
88.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
87.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
23.0ms
(* (sin a) (sin b))
15.0ms
(* r (sin b))

series594.0ms

Calls
4 calls:
Slowest
349.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
126.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
63.0ms
(* (sin a) (sin b))
56.0ms
(* r (sin b))

simplify18.0s

Calls
340 calls:
Slowest
364.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
359.0ms
(/ (* (* (* 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)))))
328.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
313.0ms
(/ (* (* (* 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)))))
287.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))

prune3.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
340×add-sqr-sqrt
276×times-frac
266×*-un-lft-identity
122×add-cube-cbrt
75×associate-*l*
73×unswap-sqr
72×distribute-lft-out-- difference-of-squares
43×associate-/r*
25×associate-/l*
21×associate-/r/
13×add-cbrt-cube add-exp-log
8×associate-/l/
7×sin-mult
6×pow1 cos-mult div-inv add-log-exp
4×cbrt-undiv div-exp insert-posit16
3×clear-num frac-2neg flip3-- associate-*r* frac-sub flip-- sub-div
1×sub-neg diff-log div-sub pow-prod-down prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
172.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r)
115.0ms
(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r))
51.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
23.0ms
(* (sin a) (sin b))

series775.0ms

Calls
4 calls:
Slowest
415.0ms
(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r))
187.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r)
110.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
62.0ms
(* (sin a) (sin b))

simplify33.9s

Calls
404 calls:
Slowest
544.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r)
404.0ms
(/ (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (* (* r r) r))
375.0ms
(- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3))
357.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
345.0ms
(- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))

prune4.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b
(* (sin a) (sin b))
0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))

rewrite493.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
117×*-un-lft-identity
70×times-frac
54×associate-*l*
47×associate-*r* unswap-sqr
42×add-cube-cbrt
36×distribute-lft-out-- difference-of-squares
32×add-exp-log
22×associate-/r*
20×add-cbrt-cube
17×associate-*r/
13×prod-exp
12×pow1
8×associate-/r/
7×cbrt-unprod sin-mult associate-/l*
6×div-exp cos-mult add-log-exp
4×pow-prod-down insert-posit16
3×cbrt-undiv rec-exp clear-num flip3-- 1-exp un-div-inv *-commutative frac-sub flip-- sub-div
2×frac-2neg div-inv
1×sub-neg diff-log pow-flip inv-pow
Calls
4 calls:
Slowest
301.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
121.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
46.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
19.0ms
(* (sin a) (sin b))

series611.0ms

Calls
4 calls:
Slowest
335.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
132.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
96.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
49.0ms
(* (sin a) (sin b))

simplify12.0s

Calls
220 calls:
Slowest
384.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
324.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
311.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
299.0ms
(* (* (* (* 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))))))
297.0ms
(* (* (* (* 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))))))

prune3.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes239.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.7s2963×body1280valid
2.0s1783×body640valid
816.0ms765×body320valid
428.0ms2130×body80valid
119.0ms361×body160valid