Details

Time bar (total: 1.3m)

sample482.0ms

Algorithm
intervals
Results
217.0ms61×body640valid
104.0ms84×body1280valid
47.0ms70×body80valid
15.0ms25×body320valid
6.0ms16×body160valid

simplify219.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
218.0ms
(* r (/ (sin b) (cos (+ a b))))

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize85.0ms

Local error

Found 3 expressions with local error:

3.2b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite113.0ms

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
56.0ms
(cos (+ a b))
29.0ms
(* r (/ (sin b) (cos (+ a b))))
25.0ms
(/ (sin b) (cos (+ a b)))

series444.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
317.0ms
(* r (/ (sin b) (cos (+ a b))))
82.0ms
(/ (sin b) (cos (+ a b)))
46.0ms
(cos (+ a b))

simplify2.4s

Counts
60 → 85
Calls
60 calls:
Slowest
412.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
273.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
261.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
258.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
209.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune892.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite219.0ms

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/
Counts
4 → 114
Calls
4 calls:
Slowest
137.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
37.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
27.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms
(* (sin a) (sin b))

series692.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
329.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
180.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
113.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
69.0ms
(* (sin a) (sin b))

simplify6.5s

Counts
86 → 126
Calls
86 calls:
Slowest
468.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
446.0ms
(* (* (* 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))))))
357.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
352.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
351.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

4.4b
(log (exp (* (sin a) (sin b))))
0.2b
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))
0.1b
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))

rewrite156.0ms

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×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u
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 → 108
Calls
4 calls:
Slowest
92.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
41.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
15.0ms
(* (sin a) (sin b))
5.0ms
(log (exp (* (sin a) (sin b))))

series622.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
319.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
165.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
78.0ms
(log (exp (* (sin a) (sin b))))
59.0ms
(* (sin a) (sin b))

simplify14.2s

Counts
83 → 120
Calls
83 calls:
Slowest
700.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
479.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))
457.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
416.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
413.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (* (cos a) (cos b)) 3)
0.3b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b
(pow (* (sin a) (sin b)) 3)
0.3b
(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))))

rewrite344.0ms

Algorithm
rewrite-expression-head
Rules
69×cos-mult
60×frac-add
57×sin-mult
49×pow1
36×add-sqr-sqrt
35×associate-/r/
30×frac-times associate-*l/ associate-*r/
28×*-un-lft-identity
27×times-frac
24×add-cbrt-cube add-exp-log
20×add-cube-cbrt
19×pow-prod-down
18×sqr-pow
16×difference-of-squares
10×prod-exp cbrt-unprod
9×associate-/l*
6×cube-div pow-unpow
4×expm1-log1p-u difference-cubes pow-pow flip3-+ pow-exp pow-sqr pow-prod-up flip-+ insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp rem-cube-cbrt associate-/l/
3×associate-/r*
2×cube-mult pow-to-exp unpow-prod-down pow-plus unpow3 cube-prod
1×pow2 cbrt-undiv clear-num frac-2neg flip3-- div-sub swap-sqr div-exp associate-*r* associate-*l* *-commutative frac-sub div-inv flip-- sub-div
Counts
4 → 186
Calls
4 calls:
Slowest
282.0ms
(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))))
42.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
8.0ms
(pow (* (sin a) (sin b)) 3)
8.0ms
(pow (* (cos a) (cos b)) 3)

series800.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
525.0ms
(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))))
117.0ms
(pow (* (sin a) (sin b)) 3)
80.0ms
(pow (* (cos a) (cos b)) 3)
78.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify31.6s

Counts
177 → 198
Calls
177 calls:
Slowest
987.0ms
(+ (* (* (* (cos a) (cos b)) (* (cos a) (cos 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)))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos 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)))))))
880.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
824.0ms
(* (* 2 2) (+ (* (* (* (sin a) (sin b)) (* (sin a) (sin 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)))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))))
776.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
715.0ms
(* 2 (+ (* (* (* (sin a) (sin b)) (* (sin a) (sin 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)))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))))

prune4.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes351.0ms

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.4s2939×body1280valid
1.7s1846×body640valid
464.0ms755×body320valid
433.0ms2103×body80valid
130.0ms358×body160valid