Details

Time bar (total: 2.1m)

sample263.0ms

Algorithm
intervals
Results
137.0ms98×body1280valid
34.0ms51×body640valid
11.0ms75×body80valid
6.0ms18×body160valid
6.0ms14×body320valid

simplify51.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize34.0ms

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))))

rewrite425.0ms

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×expm1-log1p-u clear-num associate-*l* insert-posit16 log1p-expm1-u 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
385.0ms
(cos (+ a b))
26.0ms
(* r (/ (sin b) (cos (+ a b))))
10.0ms
(/ (sin b) (cos (+ a b)))

series231.0ms

Calls
3 calls:
Slowest
136.0ms
(* r (/ (sin b) (cos (+ a b))))
58.0ms
(/ (sin b) (cos (+ a b)))
37.0ms
(cos (+ a b))

simplify2.5s

Calls
71 calls:
Slowest
420.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
301.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
288.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
242.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
213.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

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)))

rewrite458.0ms

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
256.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
98.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
71.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
23.0ms
(* (sin b) (sin a))

series624.0ms

Calls
4 calls:
Slowest
251.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
157.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
151.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
65.0ms
(* (sin b) (sin a))

simplify40.3s

Calls
491 calls:
Slowest
896.0ms
(- (* (+ (cos (+ b a)) (cos (- b a))) 2) (* 2 (- (cos (- b a)) (cos (+ b a)))))
447.0ms
(/ (* (* (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)))))
386.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos b) (cos a)) (* (sin b) (sin a)))))
383.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos b) (cos a)) (* (sin b) (sin a)))))
336.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))

prune4.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sin b) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a))))))
0.2b
(* r (/ (sin b) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a)))))))
0.2b
(* (sin b) (sin a))
0.1b
(- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a)))))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
116×add-sqr-sqrt
93×*-un-lft-identity
56×add-cube-cbrt
43×times-frac
42×associate-*r*
36×prod-diff
27×associate-*l*
18×distribute-lft-out-- difference-of-squares
16×unswap-sqr
14×associate-/r*
13×add-cbrt-cube associate-*r/ add-exp-log
12×fma-neg
8×pow1
7×associate-/l*
6×*-commutative add-log-exp
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u
3×clear-num flip3-- prod-exp cbrt-unprod flip--
2×cbrt-undiv frac-2neg div-exp pow-prod-down un-div-inv div-inv
1×sub-neg diff-log sin-mult expm1-udef associate--r-
Calls
4 calls:
Slowest
140.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a)))))))
53.0ms
(/ (sin b) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a))))))
36.0ms
(- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a)))))
23.0ms
(* (sin b) (sin a))

series845.0ms

Calls
4 calls:
Slowest
366.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a)))))))
227.0ms
(/ (sin b) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a))))))
169.0ms
(- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a)))))
82.0ms
(* (sin b) (sin a))

simplify17.1s

Calls
220 calls:
Slowest
713.0ms
(/ (exp (* (cos b) (cos a))) (exp (expm1 (log1p (* (sin b) (sin a))))))
391.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a)))))) (/ (sin b) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a))))))) (/ (sin b) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a))))))))
374.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a))))) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a)))))) (- (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a)))))))
358.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (expm1 (log1p (* (sin b) (sin a)))) (expm1 (log1p (* (sin b) (sin a))))) (* (* (cos b) (cos a)) (expm1 (log1p (* (sin b) (sin a)))))))
342.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))

prune3.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

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)))

rewrite492.0ms

Algorithm
rewrite-expression-head
Rules
296×add-sqr-sqrt
192×*-un-lft-identity
144×prod-diff
129×associate-*l*
122×associate-*r*
117×add-cube-cbrt
72×unswap-sqr
70×times-frac
36×distribute-lft-out-- difference-of-squares
32×add-exp-log
28×*-commutative
22×associate-/r*
20×add-cbrt-cube
17×associate-*r/
13×prod-exp
12×pow1 fma-neg
8×associate-/r/
7×cbrt-unprod sin-mult associate-/l*
6×div-exp cos-mult add-log-exp
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u
3×cbrt-undiv rec-exp clear-num flip3-- 1-exp un-div-inv frac-sub flip-- sub-div
2×frac-2neg div-inv
1×sub-neg diff-log pow-flip inv-pow
Calls
4 calls:
Slowest
300.0ms
(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
84.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
76.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
24.0ms
(* (sin b) (sin a))

series682.0ms

Calls
4 calls:
Slowest
326.0ms
(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
173.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
97.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
86.0ms
(* (sin b) (sin a))

simplify42.5s

Calls
518 calls:
Slowest
376.0ms
(- (* (+ (cos (+ b a)) (cos (- b a))) 2) (* 2 (- (cos (- b a)) (cos (+ b a)))))
366.0ms
(- (+ (cos (+ b a)) (cos (- b a))) (- (cos (- b a)) (cos (+ b a))))
328.0ms
(* (* (* (* r r) r) (* (* (sin b) (sin b)) (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))))))
327.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos b) (cos a)) (* (sin b) (sin a)))))
320.0ms
(fma (cos b) (cos a) (- (* (sqrt (sin a)) (* (sin b) (sqrt (sin a))))))

prune5.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes292.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
3.9s2963×body1280valid
1.9s1783×body640valid
860.0ms2130×body80valid
457.0ms765×body320valid
130.0ms361×body160valid