Details

Time bar (total: 2.3m)

sample540.0ms

Algorithm
intervals
Results
296.0ms98×body1280valid
51.0ms51×body640valid
46.0ms18×body160valid
18.0ms75×body80valid
9.0ms14×body320valid

simplify112.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize40.0ms

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))

rewrite605.0ms

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×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u 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
571.0ms
(/ (* r (sin b)) (cos (+ a b)))
21.0ms
(cos (+ a b))
10.0ms
(* r (sin b))

series236.0ms

Calls
3 calls:
Slowest
148.0ms
(/ (* r (sin b)) (cos (+ a b)))
61.0ms
(* r (sin b))
27.0ms
(cos (+ a b))

simplify3.5s

Calls
109 calls:
Slowest
305.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
220.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
219.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
205.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
199.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
378×add-sqr-sqrt
244×*-un-lft-identity
173×associate-*l*
144×prod-diff
132×times-frac add-cube-cbrt
117×associate-*r*
95×unswap-sqr
56×distribute-lft-out-- difference-of-squares
39×*-commutative
13×add-cbrt-cube add-exp-log
12×fma-neg associate-/l*
11×associate-/r*
8×pow1
6×add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult insert-posit16 log1p-expm1-u
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
113.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
71.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
16.0ms
(* r (sin b))
12.0ms
(* (sin b) (sin a))

series554.0ms

Calls
4 calls:
Slowest
285.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
146.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
83.0ms
(* (sin b) (sin a))
40.0ms
(* r (sin b))

simplify49.5s

Calls
638 calls:
Slowest
502.0ms
(- (* (+ (cos (+ b a)) (cos (- b a))) 2) (* 2 (- (cos (- b a)) (cos (+ b a)))))
470.0ms
(fma 1 (* (cos b) (cos a)) (- (* (sqrt (sin a)) (* (sin b) (sqrt (sin a))))))
394.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))
322.0ms
(- (+ (cos (+ b a)) (cos (- b a))) (- (cos (- b a)) (cos (+ b a))))
320.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos b) (cos a)) (* (sin b) (sin a)))))

prune5.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite547.0ms

Algorithm
rewrite-expression-head
Rules
280×add-sqr-sqrt
188×*-un-lft-identity
144×prod-diff
119×associate-*r*
117×associate-*l*
115×add-cube-cbrt
67×times-frac
64×unswap-sqr
36×distribute-lft-out-- difference-of-squares
27×*-commutative
22×associate-/r*
17×associate-*r/
13×add-cbrt-cube add-exp-log
12×fma-neg
8×pow1 associate-/r/
7×sin-mult associate-/l*
6×cos-mult add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×clear-num flip3-- prod-exp frac-sub cbrt-unprod flip-- sub-div
2×cbrt-undiv frac-2neg div-exp pow-prod-down un-div-inv div-inv
1×sub-neg diff-log
Calls
4 calls:
Slowest
287.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
124.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
99.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
25.0ms
(* (sin b) (sin a))

series660.0ms

Calls
4 calls:
Slowest
337.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
158.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
110.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
54.0ms
(* (sin b) (sin a))

simplify39.9s

Calls
491 calls:
Slowest
504.0ms
(fma (- (* (cbrt (sin b)) (sin a))) (* (cbrt (sin b)) (cbrt (sin b))) (* (* (cbrt (sin b)) (sin a)) (* (cbrt (sin b)) (cbrt (sin b)))))
417.0ms
(- (* (+ (cos (+ b a)) (cos (- b a))) 2) (* 2 (- (cos (- b a)) (cos (+ b a)))))
400.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos b) (cos a)) (* (sin b) (sin a))) (- (* (cos b) (cos a)) (* (sin b) (sin a)))) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
380.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos b) (cos a)) (* (sin b) (sin a)))))
355.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))

prune5.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
0.2b
(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
0.2b
(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
0.2b
(* (sin b) (sin a))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
232×add-sqr-sqrt
161×*-un-lft-identity
137×associate-*r*
105×times-frac
62×unswap-sqr
60×associate-*l* add-cube-cbrt
54×associate-*r/
48×distribute-lft-out-- difference-of-squares
34×add-exp-log
33×associate-/r*
22×add-cbrt-cube
14×pow1 prod-exp
12×associate-/r/
11×associate-/l*
8×cbrt-unprod
7×sin-mult
6×div-exp un-div-inv cos-mult
5×clear-num pow-prod-down
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp frac-2neg flip3-- 1-exp frac-sub div-inv flip-- sub-div
1×pow-flip inv-pow
Calls
4 calls:
Slowest
978.0ms
(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
260.0ms
(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
83.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
24.0ms
(* (sin b) (sin a))

series736.0ms

Calls
4 calls:
Slowest
352.0ms
(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
166.0ms
(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
146.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
73.0ms
(* (sin b) (sin a))

simplify17.0s

Calls
275 calls:
Slowest
365.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos b) (cos a)) (* (sin b) (sin a)))))
343.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos b) (cos a)) (* (sin b) (sin a)))))
327.0ms
(/ (* (* 1 1) 1) (* (* (- (* (cos b) (cos a)) (* (sin b) (sin a))) (- (* (cos b) (cos a)) (* (sin b) (sin a)))) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
323.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))
294.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos b) (cos a)) (* (sin b) (sin a)))))

prune4.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes232.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.0s2963×body1280valid
2.0s1783×body640valid
501.0ms2130×body80valid
434.0ms765×body320valid
163.0ms361×body160valid