Details

Time bar (total: 33.4s)

sample268.0ms

Algorithm
intervals
Results
111.0ms86×body1280valid
36.0ms63×body640valid
11.0ms85×body80valid
5.0ms13×body320valid
3.0ms9×body160valid

simplify56.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
56.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize36.0ms

Local error

Found 3 expressions with local error:

4.6b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1
3×associate-/r* times-frac associate-*r* associate-*l* insert-posit16 add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×cos-sum clear-num frac-2neg pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 50
Calls
3 calls:
Slowest
37.0ms
(/ (* r (sin b)) (cos (+ a b)))
20.0ms
(cos (+ a b))
13.0ms
(* r (sin b))

series220.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
144.0ms
(/ (* r (sin b)) (cos (+ a b)))
47.0ms
(* r (sin b))
28.0ms
(cos (+ a b))

simplify1.4s

Counts
33 → 59
Calls
33 calls:
Slowest
304.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
217.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
214.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
198.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
137.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune665.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize59.0ms

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)) (* (sin a) (sin b)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×associate-/r/ cos-mult insert-posit16
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×clear-num sub-neg frac-2neg diff-log div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
Slowest
54.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms
(* (sin a) (sin b))
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms
(* r (sin b))

series618.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
350.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
119.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
82.0ms
(* (sin a) (sin b))
67.0ms
(* r (sin b))

simplify3.6s

Counts
53 → 92
Calls
53 calls:
Slowest
333.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
330.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
318.0ms
(/ (* (* (* 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)))))
302.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
290.0ms
(/ (* (* (* r r) r) (* (* (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)))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

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

rewrite189.0ms

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×insert-posit16
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 diff-log associate-*r/
Counts
4 → 104
Calls
4 calls:
Slowest
95.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
33.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms
(* (sin a) (sin b))

series672.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
269.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
185.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
142.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
75.0ms
(* (sin a) (sin b))

simplify5.4s

Counts
83 → 116
Calls
83 calls:
Slowest
375.0ms
(* (* (* 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))))))
367.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
329.0ms
(/ (* (* (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)))))
312.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
290.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

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

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×associate-*l*
19×times-frac
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult
6×associate-*r* cos-mult add-log-exp
4×insert-posit16
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 diff-log associate-*l/
Counts
4 → 104
Calls
4 calls:
Slowest
132.0ms
(* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) r)
36.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
32.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms
(* (sin a) (sin b))

series732.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
403.0ms
(* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) r)
146.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
124.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms
(* (sin a) (sin b))

simplify6.8s

Counts
83 → 116
Calls
83 calls:
Slowest
431.0ms
(/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)))
411.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
401.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
395.0ms
(/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))
379.0ms
(* (* (* (/ (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))))) (* (* r r) r))

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes248.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.1s2874×body1280valid
1.7s1822×body640valid
591.0ms403×body160valid
461.0ms2164×body80valid
458.0ms739×body320valid