Details

Time bar (total: 1.2m)

sample396.0ms

Algorithm
intervals
Results
163.0ms83×body1280valid
66.0ms68×body640valid
15.0ms21×body320valid
15.0ms67×body80valid
9.0ms17×body160valid

simplify66.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
65.0ms
(* r (/ (sin b) (cos (+ a b))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize27.0ms

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))))

rewrite67.0ms

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×associate-/r* associate-*l* insert-posit16 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 → 70
Calls
3 calls:
Slowest
24.0ms
(* r (/ (sin b) (cos (+ a b))))
20.0ms
(cos (+ a b))
18.0ms
(/ (sin b) (cos (+ a b)))

series216.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
117.0ms
(* r (/ (sin b) (cos (+ a b))))
58.0ms
(/ (sin b) (cos (+ a b)))
41.0ms
(cos (+ a b))

simplify4.9s

Counts
91 → 79
Calls
91 calls:
Slowest
775.0ms
(* (* (* r (/ (sin b) (cos (+ a b)))) (* r (/ (sin b) (cos (+ a b))))) (* r (/ (sin b) (cos (+ a b)))))
428.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
330.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
227.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
227.0ms
(* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b))))

prune916.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

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))

rewrite170.0ms

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×prod-exp cbrt-unprod insert-posit16 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 → 109
Calls
4 calls:
Slowest
101.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
47.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms
(* (sin a) (sin b))
9.0ms
(* (cos a) (cos b))

series575.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
317.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
149.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
56.0ms
(* (sin a) (sin b))
53.0ms
(* (cos a) (cos b))

simplify11.0s

Counts
132 → 121
Calls
132 calls:
Slowest
450.0ms
(* r (/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))))
431.0ms
(/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)))
430.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
379.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
368.0ms
(/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

2.7b
(log (exp (* (sin a) (sin b))))
0.3b
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
0.2b
(* (sin a) (sin b))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
19×times-frac
18×associate-*r*
13×add-cbrt-cube add-exp-log
9×pow1
6×associate-*l*
5×add-log-exp
4×associate-/r/ insert-posit16
3×log-prod associate-/r* prod-exp log-pow cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative div-inv flip--
1×exp-prod clear-num frac-2neg exp-to-pow rem-log-exp associate-*r/ sin-mult
Counts
4 → 100
Calls
4 calls:
Slowest
47.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
21.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
11.0ms
(* (sin a) (sin b))
10.0ms
(log (exp (* (sin a) (sin b))))

series696.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
357.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
201.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
69.0ms
(log (exp (* (sin a) (sin b))))
68.0ms
(* (sin a) (sin b))

simplify21.3s

Counts
125 → 112
Calls
125 calls:
Slowest
580.0ms
(* (sqrt r) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))
476.0ms
(* r (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (log (exp (* (sin a) (sin b)))) 3))))
445.0ms
(/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (log (exp (* (sin a) (sin b)))) 3)))
439.0ms
(/ (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (sin b))
424.0ms
(* (* (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite292.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
32×add-sqr-sqrt
24×*-un-lft-identity
23×add-cube-cbrt
22×add-cbrt-cube
21×associate-*r*
20×times-frac
14×pow1 prod-exp
9×associate-*l*
8×associate-/r/ cbrt-unprod
6×div-exp
5×pow-prod-down sin-mult
4×associate-*r/ cos-mult insert-posit16 add-log-exp unswap-sqr
3×cbrt-undiv rec-exp associate-/r* 1-exp *-commutative associate-/l*
2×flip3-- un-div-inv frac-sub div-inv flip-- sub-div
1×clear-num frac-2neg pow-flip inv-pow
Counts
4 → 122
Calls
4 calls:
Slowest
117.0ms
(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
116.0ms
(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
45.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
11.0ms
(* (sin b) (sin a))

series678.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
306.0ms
(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
160.0ms
(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
142.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
70.0ms
(* (sin b) (sin a))

simplify16.3s

Counts
143 → 134
Calls
143 calls:
Slowest
540.0ms
(* (* (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))) (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))) (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
481.0ms
(* (* (* (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))))))
469.0ms
(* (sin b) (/ 1 (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin b) (sin a)) (* (sin b) (sin a))))))
429.0ms
(exp (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
425.0ms
(* (* (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes276.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.2s2957×body1280valid
1.7s1852×body640valid
728.0ms2117×body80valid
468.0ms739×body320valid
126.0ms338×body160valid