Details

Time bar (total: 19.0s)

sample467.0ms

Algorithm
intervals
Results
360.0ms96×body1280valid
26.0ms61×body640valid
8.0ms67×body80valid
6.0ms23×body320valid
2.0ms9×body160valid

simplify26.0ms

Counts
1 → 1
Iterations
IterNodes
done21
421
320
216
112
08

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ r (cos (+ b a)))
0.2b
(* (sin b) (/ r (cos (+ b a))))
3.9b
(cos (+ b a))

rewrite78.0ms

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:
26.0ms
(/ r (cos (+ b a)))
30.0ms
(* (sin b) (/ r (cos (+ b a))))
19.0ms
(cos (+ b a))

series301.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(/ r (cos (+ b a)))
155.0ms
(* (sin b) (/ r (cos (+ b a))))
29.0ms
(cos (+ b a))

simplify927.0ms

Counts
82 → 82
Iterations
IterNodes
done5000
21481
1287
0124

prune507.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite148.0ms

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:
13.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
18.0ms
(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
102.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
11.0ms
(* (sin a) (sin b))

series857.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
285.0ms
(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
360.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
76.0ms
(* (sin a) (sin b))

simplify1.8s

Counts
122 → 122
Iterations
IterNodes
done5000
22428
1472
0184

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin b) (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
0.2b
(* (sin b) (sin a))
0.3b
(pow (* (sin b) (sin a)) 3)
23.6b
(cbrt (pow (* (sin b) (sin a)) 3))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
16×*-un-lft-identity add-cube-cbrt
14×add-cbrt-cube add-exp-log
11×pow1
10×times-frac
8×cbrt-prod
6×associate-*l*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u sin-mult add-log-exp
3×cube-div pow-unpow pow-prod-down associate-/r/ unswap-sqr
2×cube-mult cbrt-div unpow-prod-down pow-pow unpow3 cube-prod pow-exp *-commutative rem-cube-cbrt sqr-pow
1×pow-to-exp cbrt-undiv flip3-- pow1/3 div-exp associate-*r/ cos-mult frac-sub rem-cbrt-cube div-inv flip--
Counts
4 → 103
Calls
4 calls:
100.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
16.0ms
(* (sin b) (sin a))
12.0ms
(pow (* (sin b) (sin a)) 3)
4.0ms
(cbrt (pow (* (sin b) (sin a)) 3))

series560.0ms

Counts
4 → 12
Calls
4 calls:
345.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
62.0ms
(* (sin b) (sin a))
84.0ms
(pow (* (sin b) (sin a)) 3)
68.0ms
(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.9s

Counts
115 → 115
Iterations
IterNodes
done5000
22913
1538
0197

prune880.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))) (sin b))
0.2b
(* (sin b) (sin a))
0.3b
(pow (* (sin b) (sin a)) 3)
23.6b
(cbrt (pow (* (sin b) (sin a)) 3))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*l*
16×*-un-lft-identity add-cube-cbrt
14×add-cbrt-cube add-exp-log
11×pow1
10×times-frac
8×cbrt-prod
6×associate-*r*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u sin-mult add-log-exp
3×cube-div pow-unpow pow-prod-down associate-/r/ unswap-sqr
2×cube-mult cbrt-div unpow-prod-down pow-pow unpow3 cube-prod pow-exp *-commutative rem-cube-cbrt sqr-pow
1×pow-to-exp cbrt-undiv flip3-- pow1/3 div-exp associate-*l/ cos-mult frac-sub rem-cbrt-cube div-inv flip--
Counts
4 → 103
Calls
4 calls:
96.0ms
(* (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))) (sin b))
20.0ms
(* (sin b) (sin a))
14.0ms
(pow (* (sin b) (sin a)) 3)
6.0ms
(cbrt (pow (* (sin b) (sin a)) 3))

series584.0ms

Counts
4 → 12
Calls
4 calls:
384.0ms
(* (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))) (sin b))
61.0ms
(* (sin b) (sin a))
77.0ms
(pow (* (sin b) (sin a)) 3)
61.0ms
(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.9s

Counts
115 → 115
Iterations
IterNodes
done5000
22672
1508
0187

prune706.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes264.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done18
118
015

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.0s2845×body1280valid
1.5s1942×body640valid
311.0ms2101×body80valid
256.0ms759×body320valid
79.0ms354×body160valid