Details

Time bar (total: 39.0s)

sample264.0ms

Algorithm
intervals
Results
143.0ms98×body1280valid
49.0ms62×body640valid
10.0ms69×body80valid
9.0ms18×body320valid
4.0ms9×body160valid

simplify104.0ms

Calls
1 calls:
Slowest
104.0ms
(* r (/ (sin b) (cos (+ a b))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize36.0ms

Local error

Found 3 expressions with local error:

2.8b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.1b
(* r (/ (sin b) (cos (+ a b))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Calls
3 calls:
Slowest
24.0ms
(* r (/ (sin b) (cos (+ a b))))
18.0ms
(/ (sin b) (cos (+ a b)))
17.0ms
(cos (+ a b))

series239.0ms

Calls
3 calls:
Slowest
136.0ms
(* r (/ (sin b) (cos (+ a b))))
64.0ms
(/ (sin b) (cos (+ a b)))
39.0ms
(cos (+ a b))

simplify2.4s

Calls
60 calls:
Slowest
391.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
285.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
266.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
254.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
224.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune884.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×associate-*r*
19×times-frac
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* flip3-- prod-exp frac-sub cbrt-unprod flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num sub-neg frac-2neg fma-neg diff-log prod-diff associate-*r/
Calls
4 calls:
Slowest
103.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
30.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))

series612.0ms

Calls
4 calls:
Slowest
279.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
143.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
107.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
83.0ms
(* (sin a) (sin b))

simplify6.6s

Calls
86 calls:
Slowest
512.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
502.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
350.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
342.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
340.0ms
(/ (* (* (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)))))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×*-un-lft-identity add-cube-cbrt
28×times-frac
13×add-cbrt-cube associate-*l* add-exp-log
6×pow1 associate-/r* associate-/l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp associate-*r* prod-diff div-inv
2×clear-num frac-2neg flip3-- prod-exp associate-/r/ cbrt-unprod flip-- unswap-sqr
1×sub-neg fma-neg diff-log pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
21.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
19.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
18.0ms
(* (/ (cos b) (sin b)) (cos a))
9.0ms
(/ (cos b) (sin b))

series534.0ms

Calls
4 calls:
Slowest
287.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
136.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
82.0ms
(* (/ (cos b) (sin b)) (cos a))
30.0ms
(/ (cos b) (sin b))

simplify4.9s

Calls
97 calls:
Slowest
408.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
374.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
332.0ms
(/ (* (* r r) r) (* (* (- (* (/ (cos b) (sin b)) (cos a)) (sin a)) (- (* (/ (cos b) (sin b)) (cos a)) (sin a))) (- (* (/ (cos b) (sin b)) (cos a)) (sin a))))
300.0ms
(- (/ 1 b) (+ (* 1/2 (/ (pow a 2) b)) (* 1/3 b)))
267.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube associate-*r*
18×times-frac
13×prod-exp
12×pow1
8×associate-/r/
7×cbrt-unprod sin-mult
6×div-exp cos-mult add-log-exp
4×expm1-log1p-u associate-*l* pow-prod-down insert-posit16 log1p-expm1-u
3×cbrt-undiv rec-exp associate-/r* flip3-- 1-exp frac-sub flip-- associate-/l* sub-div
2×*-commutative div-inv
1×clear-num sub-neg frac-2neg fma-neg diff-log prod-diff associate-*r/ un-div-inv pow-flip inv-pow unswap-sqr
Calls
4 calls:
Slowest
76.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
32.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
31.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
18.0ms
(* (sin a) (sin b))

series660.0ms

Calls
4 calls:
Slowest
342.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
146.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
111.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
61.0ms
(* (sin a) (sin b))

simplify7.8s

Calls
92 calls:
Slowest
393.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
361.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
334.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
313.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
310.0ms
(* (* (* (* 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))))))

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes301.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.2s2948×body1280valid
1.5s1840×body640valid
766.0ms2096×body80valid
527.0ms782×body320valid
124.0ms336×body160valid