Details

Time bar (total: 18.1s)

sample288.0ms

Algorithm
intervals
Results
141.0ms96×body1280valid
35.0ms63×body640valid
9.0ms70×body80valid
8.0ms21×body320valid
2.0ms6×body160valid

simplify32.0ms

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

prune71.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.8b

localize38.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

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:
4.0ms
(/ r (cos (+ b a)))
16.0ms
(* (sin b) (/ r (cos (+ b a))))
14.0ms
(cos (+ b a))

series325.0ms

Counts
3 → 9
Calls
3 calls:
100.0ms
(/ r (cos (+ b a)))
166.0ms
(* (sin b) (/ r (cos (+ b a))))
60.0ms
(cos (+ b a))

simplify882.0ms

Counts
82 → 82
Iterations
IterNodes
done5000
21481
1287
0124

prune499.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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

rewrite136.0ms

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)))
17.0ms
(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms
(* (sin a) (sin b))
91.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series854.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
278.0ms
(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
68.0ms
(* (sin a) (sin b))
390.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify1.8s

Counts
122 → 122
Iterations
IterNodes
done5000
22407
1472
0184

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
19×times-frac
16×associate-*l*
13×add-cbrt-cube add-exp-log
8×pow1
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* prod-exp cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num frac-2neg associate-*l/ cos-mult fma-udef
Counts
4 → 94
Calls
4 calls:
8.0ms
(* (cos a) (cos b))
0.0ms
(fma (sin a) (- (sin b)) (* (cos a) (cos b)))
19.0ms
(* (/ (sin b) (fma (sin a) (- (sin b)) (* (cos a) (cos b)))) r)
11.0ms
(/ (sin b) (fma (sin a) (- (sin b)) (* (cos a) (cos b))))

series750.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (cos a) (cos b))
123.0ms
(fma (sin a) (- (sin b)) (* (cos a) (cos b)))
380.0ms
(* (/ (sin b) (fma (sin a) (- (sin b)) (* (cos a) (cos b)))) r)
178.0ms
(/ (sin b) (fma (sin a) (- (sin b)) (* (cos a) (cos b))))

simplify980.0ms

Counts
106 → 106
Iterations
IterNodes
done5000
21604
1378
0165

prune786.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
19×times-frac
18×associate-*r*
13×add-cbrt-cube add-exp-log
8×pow1
6×associate-*l*
5×expm1-log1p-u
4×associate-/r/ log1p-expm1-u add-log-exp
3×associate-/r* prod-exp cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative div-inv flip--
1×log1p-udef clear-num frac-2neg log1p-expm1 associate-*r/ sin-mult
Counts
4 → 99
Calls
4 calls:
1.0ms
(log1p (* (sin a) (sin b)))
18.0ms
(/ r (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
9.0ms
(* (sin a) (sin b))
53.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))

series984.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(log1p (* (sin a) (sin b)))
374.0ms
(/ r (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
57.0ms
(* (sin a) (sin b))
400.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))

simplify1.5s

Counts
111 → 111
Iterations
IterNodes
done5000
22327
1452
0182

prune780.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes320.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done17
117
014

end0.0ms

sample5.9s

Algorithm
intervals
Results
3.6s2945×body1280valid
1.2s1803×body640valid
310.0ms2112×body80valid
303.0ms773×body320valid
85.0ms367×body160valid