Details

Time bar (total: 54.2s)

sample552.0ms

Algorithm
intervals
Results
269.0ms98×body1280valid
107.0ms51×body640valid
15.0ms75×body80valid
7.0ms18×body160valid
7.0ms14×body320valid

simplify45.0ms

Calls
1 calls:
Slowest
44.0ms
(* r (/ (sin b) (cos (+ a b))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize47.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
19×times-frac
13×associate-*r*
10×add-cbrt-cube add-exp-log
9×associate-*r/
7×associate-/l*
6×associate-/r*
5×pow1
3×clear-num associate-*l* insert-posit16 add-log-exp
2×cbrt-undiv cos-sum frac-2neg div-exp prod-exp un-div-inv cbrt-unprod div-inv unswap-sqr
1×+-commutative pow-prod-down *-commutative
Calls
3 calls:
Slowest
18.0ms
(* r (/ (sin b) (cos (+ a b))))
13.0ms
(cos (+ a b))
10.0ms
(/ (sin b) (cos (+ a b)))

series204.0ms

Calls
3 calls:
Slowest
123.0ms
(* r (/ (sin b) (cos (+ a b))))
45.0ms
(/ (sin b) (cos (+ a b)))
36.0ms
(cos (+ a b))

simplify2.3s

Calls
71 calls:
Slowest
454.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
269.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
250.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
206.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
152.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune946.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

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)))

rewrite446.0ms

Algorithm
rewrite-expression-head
Rules
155×add-sqr-sqrt
113×*-un-lft-identity
67×times-frac
44×associate-*r*
42×associate-*l*
40×add-cube-cbrt
39×unswap-sqr
36×distribute-lft-out-- difference-of-squares
22×associate-/r*
17×associate-*r/
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult associate-/l*
6×cos-mult add-log-exp
4×insert-posit16
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 *-commutative div-inv
1×sub-neg diff-log
Calls
4 calls:
Slowest
287.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
94.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
41.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
20.0ms
(* (sin b) (sin a))

series715.0ms

Calls
4 calls:
Slowest
320.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
185.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
134.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
76.0ms
(* (sin b) (sin a))

simplify9.5s

Calls
193 calls:
Slowest
391.0ms
(/ (* (* (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)))))
356.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
322.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))
317.0ms
(- (+ (cos (+ b a)) (cos (- b a))) (- (cos (- b a)) (cos (+ b a))))
307.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos b) (cos a)) (* (sin b) (sin a)))))

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite461.0ms

Algorithm
rewrite-expression-head
Rules
155×add-sqr-sqrt
113×*-un-lft-identity
67×times-frac
44×associate-*r*
42×associate-*l*
40×add-cube-cbrt
39×unswap-sqr
36×distribute-lft-out-- difference-of-squares
22×associate-/r*
17×associate-*r/
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult associate-/l*
6×cos-mult add-log-exp
4×insert-posit16
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 *-commutative div-inv
1×sub-neg diff-log
Calls
4 calls:
Slowest
302.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
79.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
53.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
23.0ms
(* (sin b) (sin a))

series571.0ms

Calls
4 calls:
Slowest
251.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
136.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
101.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
83.0ms
(* (sin b) (sin a))

simplify9.3s

Calls
193 calls:
Slowest
392.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))
391.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))))
332.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (* (sin b) (sin a))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
297.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- b a)) (cos (+ b a)))))
288.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos a) (cos b)) (* (sin b) (sin a)))))

prune2.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite475.0ms

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
303.0ms
(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
93.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
51.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
22.0ms
(* (sin b) (sin a))

series634.0ms

Calls
4 calls:
Slowest
294.0ms
(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
144.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
136.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
59.0ms
(* (sin b) (sin a))

simplify12.1s

Calls
220 calls:
Slowest
410.0ms
(/ (sqrt 1) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
358.0ms
(- (+ (cos (+ b a)) (cos (- b a))) (- (cos (- b a)) (cos (+ b a))))
333.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))
315.0ms
(- (* (+ (cos (+ b a)) (cos (- b a))) 2) (* 2 (- (cos (- b a)) (cos (+ b a)))))
282.0ms
(* (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (/ (* (* 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))))))

prune3.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes330.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample7.0s

Algorithm
intervals
Results
3.9s2963×body1280valid
1.8s1783×body640valid
492.0ms2130×body80valid
425.0ms765×body320valid
159.0ms361×body160valid