Details

Time bar (total: 21.3s)

sample490.0ms

Algorithm
intervals
Results
258.0ms83×body1280valid
54.0ms68×body640valid
13.0ms21×body320valid
13.0ms67×body80valid
8.0ms17×body160valid

simplify37.0ms

Counts
1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize24.0ms

Local error

Found 3 expressions with local error:

3.5b
(cos (+ a b))
0.3b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite59.0ms

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
34.0ms
(cos (+ a b))
13.0ms
(* r (/ (sin b) (cos (+ a b))))
10.0ms
(/ (sin b) (cos (+ a b)))

series510.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
351.0ms
(* r (/ (sin b) (cos (+ a b))))
133.0ms
(/ (sin b) (cos (+ a b)))
26.0ms
(cos (+ a b))

simplify524.0ms

Counts
97 → 85

prune762.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

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))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
23×associate-*r*
19×times-frac
15×add-cbrt-cube add-exp-log
10×pow1
9×associate-*l*
8×associate-/r/
5×cos-mult sin-mult
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r* pow-prod-down *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp frac-sub div-inv flip-- sub-div
1×clear-num frac-2neg associate-*r/
Counts
4 → 117
Calls
4 calls:
Slowest
76.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
41.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
15.0ms
(* (cos a) (cos b))
11.0ms
(* (sin a) (sin b))

series584.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
316.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
147.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
72.0ms
(* (sin a) (sin b))
50.0ms
(* (cos a) (cos b))

simplify672.0ms

Counts
140 → 129

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize123.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b
(* (* (cos b) (cos a)) (* (cos b) (cos a)))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b
(* (* (sin b) (sin a)) (* (sin b) (sin a)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
160×pow1
68×pow-prod-down
52×add-cbrt-cube add-exp-log
32×prod-exp cbrt-unprod
16×pow-sqr pow-prod-up
8×pow-plus cos-mult sin-mult
4×pow2 add-sqr-sqrt expm1-log1p-u frac-times *-un-lft-identity swap-sqr associate-*r* associate-*l* associate-*l/ associate-*r/ *-commutative add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 160
Calls
4 calls:
Slowest
86.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
57.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
52.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
41.0ms
(* (* (cos b) (cos a)) (* (cos b) (cos a)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
84.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
67.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
64.0ms
(* (* (cos b) (cos a)) (* (cos b) (cos a)))

simplify597.0ms

Counts
172 → 172

prune3.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (* (cos a) (cos b)))
0.3b
(log1p (expm1 (* (cos a) (cos b))))
0.3b
(/ (sin b) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b))))
0.2b
(* r (/ (sin b) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b)))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
19×times-frac
15×associate-*r*
11×add-cbrt-cube add-exp-log
6×pow1
5×log1p-expm1-u
4×expm1-log1p-u associate-/r/ insert-posit16 add-log-exp
3×associate-/r* associate-*l* associate-/l*
2×cbrt-undiv flip3-- div-exp prod-exp cbrt-unprod div-inv flip-- unswap-sqr
1×log1p-udef expm1-log1p clear-num frac-2neg pow-prod-down log1p-expm1 associate-*r/ *-commutative expm1-udef
Counts
4 → 93
Calls
4 calls:
Slowest
32.0ms
(* r (/ (sin b) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b)))))
23.0ms
(/ (sin b) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b))))
1.0ms
(expm1 (* (cos a) (cos b)))
0.0ms
(log1p (expm1 (* (cos a) (cos b))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
572.0ms
(/ (sin b) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b))))
325.0ms
(* r (/ (sin b) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b)))))
106.0ms
(expm1 (* (cos a) (cos b)))
90.0ms
(log1p (expm1 (* (cos a) (cos b))))

simplify477.0ms

Counts
114 → 105

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes372.0ms

Accuracy

0% (0.3b remaining)

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

bsearch11.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.6s2957×body1280valid
1.7s1852×body640valid
508.0ms739×body320valid
452.0ms2117×body80valid
139.0ms338×body160valid