Details

Time bar (total: 30.9s)

sample327.0ms

Algorithm
intervals
Results
112.0ms84×body1280valid
57.0ms19×body160valid
53.0ms61×body640valid
17.0ms72×body80valid
12.0ms20×body320valid

simplify78.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
77.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize37.0ms

Local error

Found 3 expressions with local error:

2.6b
(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×expm1-log1p-u associate-/r* times-frac associate-*r* associate-*l* insert-posit16 log1p-expm1-u 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 → 56
Calls
3 calls:
Slowest
29.0ms
(* r (sin b))
24.0ms
(/ (* r (sin b)) (cos (+ a b)))
18.0ms
(cos (+ a b))

series209.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
144.0ms
(/ (* r (sin b)) (cos (+ a b)))
39.0ms
(* r (sin b))
25.0ms
(cos (+ a b))

simplify1.5s

Counts
33 → 65
Calls
33 calls:
Slowest
258.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
243.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
236.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
221.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
219.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune758.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

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)))

rewrite80.0ms

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
27.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
18.0ms
(* (sin a) (sin b))
16.0ms
(* r (sin b))

series611.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
349.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
135.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
75.0ms
(* (sin a) (sin b))
52.0ms
(* r (sin b))

simplify3.9s

Counts
56 → 102
Calls
56 calls:
Slowest
406.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
362.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
347.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
344.0ms
(/ (* (* (* 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)))))
337.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))
0.1b
(* r (sin b))
0.1b
(log1p (* (sin a) (sin b)))

rewrite54.0ms

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*
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down associate-/r/ *-commutative unswap-sqr
1×log1p-udef clear-num frac-2neg flip3-- log1p-expm1 div-inv flip-- sin-mult associate-/l*
Counts
4 → 81
Calls
4 calls:
Slowest
30.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
11.0ms
(* (sin a) (sin b))
10.0ms
(* r (sin b))
1.0ms
(log1p (* (sin a) (sin b)))

series601.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
383.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
104.0ms
(log1p (* (sin a) (sin b)))
65.0ms
(* (sin a) (sin b))
50.0ms
(* r (sin b))

simplify3.0s

Counts
49 → 93
Calls
49 calls:
Slowest
354.0ms
(- (* a b) (+ (* 1/2 (* (pow a 2) (pow b 2))) (* 1/6 (* (pow a 3) b))))
304.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
299.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))
280.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
278.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (expm1 (log1p (* (sin a) (sin b)))) (expm1 (log1p (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

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)))

rewrite193.0ms

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
99.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
41.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
35.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms
(* (sin a) (sin b))

series707.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
342.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
158.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
119.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
88.0ms
(* (sin a) (sin b))

simplify6.4s

Counts
86 → 126
Calls
86 calls:
Slowest
511.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
408.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
379.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
363.0ms
(/ (* (* (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)))))
354.0ms
(* (* (* 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))))))

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes261.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.5s2853×body1280valid
1.9s1834×body640valid
464.0ms790×body320valid
443.0ms2159×body80valid
135.0ms365×body160valid