Details

Time bar (total: 35.7s)

sample321.0ms

Algorithm
intervals
Results
77.0ms92×body1280valid
66.0ms58×body640valid
14.0ms25×body320valid
8.0ms69×body80valid
3.0ms12×body160valid

simplify33.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
32.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize20.0ms

Local error

Found 3 expressions with local error:

4.1b
(cos (+ a b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite50.0ms

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
23.0ms
(cos (+ a b))
14.0ms
(/ (* r (sin b)) (cos (+ a b)))
9.0ms
(* r (sin b))

series366.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
224.0ms
(/ (* r (sin b)) (cos (+ a b)))
116.0ms
(* r (sin b))
26.0ms
(cos (+ a b))

simplify1.7s

Counts
33 → 59
Calls
33 calls:
Slowest
383.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
219.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
219.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
211.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
169.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune763.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

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)) (* (sin a) (sin b)))
0.1b
(* r (sin b))

rewrite81.0ms

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
38.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series618.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
334.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
137.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
77.0ms
(* (sin a) (sin b))
70.0ms
(* r (sin b))

simplify3.4s

Counts
53 → 92
Calls
53 calls:
Slowest
338.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
315.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
304.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
289.0ms
(/ (* (* (* 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)))))
252.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

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

rewrite171.0ms

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
106.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms
(* (sin a) (sin b))

series688.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
351.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
162.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
98.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
76.0ms
(* (sin a) (sin b))

simplify6.1s

Counts
83 → 116
Calls
83 calls:
Slowest
676.0ms
(* (* (* 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))))))
438.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
351.0ms
(- (* (+ (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))))))
335.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))
0.1b
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite248.0ms

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
100.0ms
(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
94.0ms
(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
39.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms
(* (sin a) (sin b))

series681.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
276.0ms
(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
175.0ms
(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
170.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
60.0ms
(* (sin a) (sin b))

simplify7.6s

Counts
101 → 134
Calls
101 calls:
Slowest
562.0ms
(* (* (* (sin b) (sin b)) (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))))))
417.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
309.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
300.0ms
(* (* (* r r) r) (* (* (* (sin b) (sin b)) (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)))))))
298.0ms
(/ (* (* 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)))))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes272.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.1s2930×body1280valid
1.7s1849×body640valid
944.0ms2131×body80valid
419.0ms771×body320valid
117.0ms322×body160valid