Details

Time bar (total: 35.3s)

sample340.0ms

Algorithm
intervals
Results
105.0ms86×body1280valid
91.0ms63×body640valid
15.0ms85×body80valid
7.0ms13×body320valid
3.0ms9×body160valid

simplify68.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
67.0ms
(* r (/ (sin b) (cos (+ a b))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize42.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

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
25.0ms
(* r (/ (sin b) (cos (+ a b))))
18.0ms
(/ (sin b) (cos (+ a b)))
17.0ms
(cos (+ a b))

series237.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
115.0ms
(* r (/ (sin b) (cos (+ a b))))
71.0ms
(/ (sin b) (cos (+ a b)))
50.0ms
(cos (+ a b))

simplify2.3s

Counts
60 → 79
Calls
60 calls:
Slowest
447.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
278.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
231.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
199.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
188.0ms
(* (* (* r r) r) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b)))))

prune920.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize61.0ms

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)))

rewrite184.0ms

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
99.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
37.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
35.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms
(* (sin a) (sin b))

series674.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
288.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
177.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
128.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
81.0ms
(* (sin a) (sin b))

simplify6.1s

Counts
83 → 116
Calls
83 calls:
Slowest
509.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
441.0ms
(/ (* (* (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)))))
430.0ms
(* (* (* 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))))))
326.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
326.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

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)))

rewrite91.0ms

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
34.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
33.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series585.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
338.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
133.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
64.0ms
(* (sin a) (sin b))
49.0ms
(* r (sin b))

simplify3.8s

Counts
53 → 92
Calls
53 calls:
Slowest
375.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
366.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
359.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
332.0ms
(/ (* (* (* 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)))))
298.0ms
(/ (* (* (* 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)))))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.2b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(* (sin a) (sin b))
0.2b
(* (sin a) (sin b))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
36×pow-prod-down
32×add-cbrt-cube add-exp-log
18×prod-exp cbrt-unprod
12×add-sqr-sqrt
8×*-un-lft-identity associate-*r* associate-*l* pow-sqr pow-prod-up add-cube-cbrt
6×sin-mult
4×pow-plus cos-mult *-commutative insert-posit16 add-log-exp
2×pow2 frac-times swap-sqr associate-*l/ associate-*r/ unswap-sqr
Counts
4 → 116
Calls
4 calls:
Slowest
59.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
44.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
22.0ms
(* (sin a) (sin b))
21.0ms
(* (sin a) (sin b))

series310.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
94.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
80.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
71.0ms
(* (sin a) (sin b))
66.0ms
(* (sin a) (sin b))

simplify6.6s

Counts
108 → 128
Calls
108 calls:
Slowest
971.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
937.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
684.0ms
(* (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))))
637.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
310.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes299.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
3.8s2874×body1280valid
1.9s1822×body640valid
917.0ms739×body320valid
410.0ms2164×body80valid
167.0ms403×body160valid