Details

Time bar (total: 51.9s)

sample272.0ms

Algorithm
intervals
Results
76.0ms83×body1280valid
69.0ms68×body640valid
10.0ms21×body320valid
9.0ms67×body80valid
5.0ms17×body160valid

simplify38.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
37.0ms
(* r (/ (sin b) (cos (+ a b))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize81.0ms

Local error

Found 3 expressions with local error:

3.5b
(cos (+ a b))
0.3b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite143.0ms

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
Counts
3 → 76
Calls
3 calls:
Slowest
66.0ms
(* r (/ (sin b) (cos (+ a b))))
45.0ms
(cos (+ a b))
26.0ms
(/ (sin b) (cos (+ a b)))

series301.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
195.0ms
(* r (/ (sin b) (cos (+ a b))))
61.0ms
(/ (sin b) (cos (+ a b)))
44.0ms
(cos (+ a b))

simplify4.9s

Counts
97 → 85
Calls
97 calls:
Slowest
528.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
316.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
268.0ms
(* (* (* r (/ (sin b) (cos (+ a b)))) (* r (/ (sin b) (cos (+ a b))))) (* r (/ (sin b) (cos (+ a b)))))
266.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
259.0ms
(* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b))))

prune990.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (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))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
23×associate-*r*
19×times-frac
15×add-cbrt-cube add-exp-log
10×pow1
9×associate-*l*
8×associate-/r/
5×cos-mult sin-mult
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r* pow-prod-down *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp frac-sub div-inv flip-- sub-div
1×clear-num frac-2neg associate-*r/
Counts
4 → 117
Calls
4 calls:
Slowest
114.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))
18.0ms
(* (cos a) (cos b))

series606.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
182.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
79.0ms
(* (cos a) (cos b))
54.0ms
(* (sin a) (sin b))

simplify11.9s

Counts
140 → 129
Calls
140 calls:
Slowest
713.0ms
(* (* (* 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))))))
502.0ms
(/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b))))))
398.0ms
(/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))
397.0ms
(* r (/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))))
381.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-cbrt-cube add-exp-log
12×*-un-lft-identity add-cube-cbrt
10×pow1
9×associate-*r* associate-*l*
4×expm1-log1p-u prod-exp associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac pow-prod-down cos-mult *-commutative sin-mult unswap-sqr
2×cbrt-undiv div-exp
1×clear-num frac-2neg flip3-- frac-sub div-inv flip-- associate-/l* sub-div
Counts
4 → 93
Calls
4 calls:
Slowest
60.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))
17.0ms
(* r (sin b))
13.0ms
(* (cos a) (cos b))

series524.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
362.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
59.0ms
(* (sin a) (sin b))
57.0ms
(* r (sin b))
46.0ms
(* (cos a) (cos b))

simplify8.2s

Counts
109 → 105
Calls
109 calls:
Slowest
426.0ms
(* (* (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
426.0ms
(/ (* r (sin b)) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))
414.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
349.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
348.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

26.5b
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(* (sin a) (sin b))
0.2b
(* (sin a) (sin b))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
20×add-cbrt-cube add-exp-log
19×pow-prod-down
18×sin-mult
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×cbrt-div associate-*r* associate-*l*
6×frac-times associate-*l/
4×expm1-log1p-u associate-*r/ pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-plus unswap-sqr
1×cbrt-prod pow2 pow1/3 swap-sqr pow3 rem-cbrt-cube
Counts
4 → 104
Calls
4 calls:
Slowest
196.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
55.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
23.0ms
(* (sin a) (sin b))
11.0ms
(* (sin a) (sin b))

series284.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
74.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
64.0ms
(* (sin a) (sin b))
60.0ms
(* (sin a) (sin b))

simplify10.1s

Counts
122 → 116
Calls
122 calls:
Slowest
789.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
762.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
382.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
371.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
357.0ms
(cbrt (* (* (- (cos (- a b)) (cos (+ a b))) (- (cos (- a b)) (cos (+ a b)))) (- (cos (- a b)) (cos (+ a b)))))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes297.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
3.8s2957×body1280valid
1.6s1852×body640valid
915.0ms739×body320valid
592.0ms338×body160valid
424.0ms2117×body80valid