Details

Time bar (total: 56.8s)

sample383.0ms

Algorithm
intervals
Results
195.0ms93×body1280valid
55.0ms56×body640valid
21.0ms30×body320valid
15.0ms69×body80valid
4.0ms8×body160valid

simplify332.0ms

Calls
1 calls:
Slowest
331.0ms
(* r (/ (sin b) (cos (+ a b))))

prune62.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize45.0ms

Local error

Found 3 expressions with local error:

2.9b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
5×add-cbrt-cube add-exp-log
3×pow1 associate-/r* insert-posit16 associate-/l* add-log-exp
2×div-inv
1×cbrt-undiv cos-sum clear-num frac-2neg div-exp associate-*r/ *-commutative
Calls
3 calls:
Slowest
6.0ms
(cos (+ a b))
5.0ms
(/ (sin b) (cos (+ a b)))
4.0ms
(* r (/ (sin b) (cos (+ a b))))

series265.0ms

Calls
3 calls:
Slowest
140.0ms
(* r (/ (sin b) (cos (+ a b))))
75.0ms
(/ (sin b) (cos (+ a b)))
50.0ms
(cos (+ a b))

simplify1.5s

Calls
49 calls:
Slowest
302.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
233.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
205.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
165.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
60.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))

prune968.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×associate-*r*
18×times-frac
8×add-cbrt-cube add-exp-log associate-/r/
7×sin-mult
6×pow1 cos-mult add-log-exp
4×insert-posit16
3×associate-/r* flip3-- associate-*l* frac-sub flip-- associate-/l* sub-div
2×*-commutative div-inv
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp pow-prod-down prod-exp associate-*r/ cbrt-unprod
Calls
4 calls:
Slowest
29.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
27.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
11.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms
(* (sin a) (sin b))

series651.0ms

Calls
4 calls:
Slowest
320.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
163.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
103.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
65.0ms
(* (sin a) (sin b))

simplify4.4s

Calls
70 calls:
Slowest
441.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
349.0ms
(/ (* (* (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)))))
316.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
270.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
259.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b
(* (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
60×pow1
42×cos-mult sin-mult
35×add-cbrt-cube add-exp-log
34×associate-*l*
32×associate-/r/
27×pow-prod-down
25×associate-*r/
24×times-frac
23×associate-*l/
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×frac-times
18×prod-exp frac-sub cbrt-unprod
10×sub-div
8×pow-prod-up
7×difference-of-squares
5×associate-*r*
4×associate-/r* pow-plus insert-posit16 add-log-exp
3×*-commutative associate-/l*
2×pow2 cbrt-undiv flip3-+ flip3-- div-exp frac-add flip-+ div-inv flip--
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in
Calls
4 calls:
Slowest
135.0ms
(* (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
82.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
37.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
33.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series696.0ms

Calls
4 calls:
Slowest
346.0ms
(* (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
186.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
85.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
79.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify29.6s

Calls
161 calls:
Slowest
1.2s
(* (/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (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)))))
912.0ms
(/ (sqrt (sin b)) (sqrt (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
718.0ms
(* (* (* (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))) (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (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)))))
689.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
685.0ms
(* (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

prune3.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×pow1 associate-*r* add-log-exp
5×sin-mult
4×associate-/r/ cos-mult insert-posit16
3×associate-/r* times-frac associate-*l*
2×flip3-- *-commutative frac-sub flip-- sub-div
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp pow-prod-down prod-exp cbrt-unprod div-inv associate-/l*
Calls
4 calls:
Slowest
12.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms
(* (sin a) (sin b))
1.0ms
(* r (sin b))

series555.0ms

Calls
4 calls:
Slowest
305.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
122.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
73.0ms
(* (sin a) (sin b))
54.0ms
(* r (sin b))

simplify2.7s

Calls
42 calls:
Slowest
364.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
355.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
288.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
285.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
217.0ms
(/ (* (* (* 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)))))

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes291.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch5.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
3.8s2906×body1280valid
2.5s1842×body640valid
496.0ms739×body320valid
411.0ms2184×body80valid
170.0ms330×body160valid