Details

Time bar (total: 27.0s)

sample490.0ms

Algorithm
intervals
Results
157.0ms92×body1280valid
74.0ms26×body320valid
53.0ms53×body640valid
15.0ms74×body80valid
5.0ms11×body160valid

simplify68.0ms

Counts
1 → 1

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize61.0ms

Local error

Found 3 expressions with local error:

3.5b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite66.0ms

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
28.0ms
(* r (/ (sin b) (cos (+ a b))))
17.0ms
(/ (sin b) (cos (+ a b)))
16.0ms
(cos (+ a b))

series254.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
148.0ms
(* r (/ (sin b) (cos (+ a b))))
58.0ms
(cos (+ a b))
48.0ms
(/ (sin b) (cos (+ a b)))

simplify855.0ms

Counts
85 → 85

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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)))

rewrite169.0ms

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
89.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
35.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(* (sin a) (sin b))

series697.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
330.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
183.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
115.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
69.0ms
(* (sin a) (sin b))

simplify1.9s

Counts
126 → 126

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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

rewrite93.0ms

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×expm1-log1p-u associate-/r/ cos-mult insert-posit16 log1p-expm1-u
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 fma-neg diff-log prod-diff div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
Slowest
33.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms
(* r (sin b))
16.0ms
(* (sin a) (sin b))

series564.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
321.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
127.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
61.0ms
(* (sin a) (sin b))
55.0ms
(* r (sin b))

simplify2.0s

Counts
102 → 102

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(/ (* r (sin b)) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
0.2b
(* (/ (* r (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))))

rewrite764.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
42×add-cbrt-cube add-exp-log cos-mult sin-mult
35×pow-prod-down
32×associate-/r/
26×associate-*l*
25×associate-*r/
23×associate-*l/
21×frac-times prod-exp cbrt-unprod
18×frac-sub
11×add-sqr-sqrt
10×sub-div
9×*-un-lft-identity add-cube-cbrt
8×times-frac pow-sqr pow-prod-up
5×associate-*r*
4×expm1-log1p-u cbrt-undiv associate-/r* pow-plus div-exp insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative difference-of-squares
2×pow2 flip3-+ flip3-- swap-sqr frac-add flip-+ div-inv flip--
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in associate-/l* unswap-sqr
Counts
4 → 177
Calls
4 calls:
Slowest
492.0ms
(* (/ (* r (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))))
138.0ms
(/ (* r (sin b)) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
77.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
52.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
640.0ms
(* (/ (* r (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))))
399.0ms
(/ (* r (sin b)) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
100.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
74.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify2.4s

Counts
189 → 189

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes270.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.9s2981×body1280valid
1.6s1785×body640valid
460.0ms779×body320valid
437.0ms2101×body80valid
129.0ms357×body160valid