Details

Time bar (total: 31.2s)

sample312.0ms

Algorithm
intervals
Results
81.0ms82×body1280valid
59.0ms27×body320valid
36.0ms67×body640valid
9.0ms65×body80valid
5.0ms15×body160valid

simplify56.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
55.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize18.0ms

Local error

Found 3 expressions with local error:

3.6b
(cos (+ a b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite40.0ms

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
19.0ms
(cos (+ a b))
11.0ms
(/ (* r (sin b)) (cos (+ a b)))
7.0ms
(* r (sin b))

series210.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
112.0ms
(/ (* r (sin b)) (cos (+ a b)))
69.0ms
(* r (sin b))
28.0ms
(cos (+ a b))

simplify1.5s

Counts
33 → 59
Calls
33 calls:
Slowest
310.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
240.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
215.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
181.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
171.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune655.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 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)))

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
32.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
26.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms
(* r (sin b))
12.0ms
(* (sin a) (sin b))

series591.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
341.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
127.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
65.0ms
(* r (sin b))
58.0ms
(* (sin a) (sin b))

simplify3.7s

Counts
53 → 92
Calls
53 calls:
Slowest
355.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
324.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
323.0ms
(/ (* (* (* 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)))))
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)))))
301.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

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)))

rewrite143.0ms

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
86.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
24.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms
(* (sin a) (sin b))

series691.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
303.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
160.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
153.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
75.0ms
(* (sin a) (sin b))

simplify5.9s

Counts
83 → 116
Calls
83 calls:
Slowest
514.0ms
(+ (log r) (log (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
368.0ms
(* (* (* 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))))))
342.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
321.0ms
(/ (* (* (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)))))
303.0ms
(+ (* (* (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

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity times-frac add-cube-cbrt
13×add-cbrt-cube associate-*l* add-exp-log
6×pow1 associate-/r* associate-/l* add-log-exp
4×insert-posit16
3×cbrt-undiv div-exp associate-*r* div-inv
2×clear-num frac-2neg flip3-- prod-exp associate-/r/ cbrt-unprod flip-- unswap-sqr
1×sub-neg diff-log pow-prod-down associate-*l/ *-commutative
Counts
4 → 104
Calls
4 calls:
Slowest
43.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
28.0ms
(* (/ (cos b) (sin b)) (cos a))
27.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
17.0ms
(/ (cos b) (sin b))

series490.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
276.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
99.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
79.0ms
(* (/ (cos b) (sin b)) (cos a))
36.0ms
(/ (cos b) (sin b))

simplify4.5s

Counts
90 → 116
Calls
90 calls:
Slowest
431.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
360.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
347.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
325.0ms
(/ (* (* r r) r) (* (* (- (* (/ (cos b) (sin b)) (cos a)) (sin a)) (- (* (/ (cos b) (sin b)) (cos a)) (sin a))) (- (* (/ (cos b) (sin b)) (cos a)) (sin a))))
292.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes265.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.2s2906×body1280valid
2.0s1876×body640valid
478.0ms794×body320valid
326.0ms2071×body80valid
166.0ms357×body160valid