Details

Time bar (total: 20.6s)

sample674.0ms

Algorithm
intervals
Results
90.0ms97×body1280valid
29.0ms51×body640valid
12.0ms23×body320valid
9.0ms72×body80valid
4.0ms13×body160valid

simplify24.0ms

Counts
1 → 1
Iterations
IterNodes
done21
521
420
318
216
112
08

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.2b
(/ (sin b) (cos (+ a b)))
4.1b
(cos (+ a b))

rewrite51.0ms

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* 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 → 73
Calls
3 calls:
16.0ms
(* r (/ (sin b) (cos (+ a b))))
8.0ms
(/ (sin b) (cos (+ a b)))
11.0ms
(cos (+ a b))

series254.0ms

Counts
3 → 9
Calls
3 calls:
161.0ms
(* r (/ (sin b) (cos (+ a b))))
54.0ms
(/ (sin b) (cos (+ a b)))
39.0ms
(cos (+ a b))

simplify2.2s

Counts
82 → 82
Iterations
IterNodes
done5012
33284
2879
1280
0123

prune531.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite173.0ms

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 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 → 110
Calls
4 calls:
28.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
91.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
27.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms
(* (sin a) (sin b))

series790.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
384.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
178.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
89.0ms
(* (sin a) (sin b))

simplify1.8s

Counts
122 → 122
Iterations
IterNodes
done5001
21531
1462
0182

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
19×times-frac
18×associate-*r*
13×add-cbrt-cube add-exp-log
8×pow1
6×associate-*l* add-log-exp
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×associate-/r* flip3-- prod-diff prod-exp cbrt-unprod flip-- associate-/l* unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num sub-neg frac-2neg fma-neg diff-log associate-*r/ sin-mult expm1-udef associate--r-
Counts
4 → 107
Calls
4 calls:
20.0ms
(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
53.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))
23.0ms
(/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
15.0ms
(* (sin a) (sin b))

series926.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
419.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))
276.0ms
(/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
60.0ms
(* (sin a) (sin b))

simplify1.9s

Counts
119 → 119
Iterations
IterNodes
done5001
21525
1468
0193

prune993.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

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 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 → 86
Calls
4 calls:
16.0ms
(* (sin b) r)
25.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms
(* (sin a) (sin b))
30.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series699.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sin b) r)
150.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
78.0ms
(* (sin a) (sin b))
405.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.5s

Counts
98 → 98
Iterations
IterNodes
done5000
21250
1389
0152

prune796.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes400.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done19
119
015

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.9s2936×body1280valid
975.0ms1824×body640valid
712.0ms2074×body80valid
367.0ms840×body320valid
67.0ms327×body160valid