Details

Time bar (total: 20.0s)

sample829.0ms

Algorithm
intervals
Results
57.0ms94×body1280valid
26.0ms62×body640valid
6.0ms21×body320valid
6.0ms68×body80valid
4.0ms11×body160valid

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
08243
112243
216243
320243
421243
done21243

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize38.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))
2.2b
(cos (+ a b))

rewrite85.0ms

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
(/ (sin b) (cos (+ a b)))
29.0ms
(* r (/ (sin b) (cos (+ a b))))
18.0ms
(cos (+ a b))

series249.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(/ (sin b) (cos (+ a b)))
166.0ms
(* r (/ (sin b) (cos (+ a b))))
43.0ms
(cos (+ a b))

simplify1.2s

Counts
82 → 82
Iterations

Useful iterations: done (1.2s)

IterNodesCost
012325254
128323572
2107523330
done500123195

prune582.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite159.0ms

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:
15.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
32.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
97.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms
(* (sin a) (sin b))

series678.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
163.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
335.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
54.0ms
(* (sin a) (sin b))

simplify2.0s

Counts
122 → 122
Iterations

Useful iterations: done (2.0s)

IterNodesCost
018255979
146753188
2195852731
done500151762

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
19×times-frac
16×associate-*r*
13×add-cbrt-cube add-exp-log
8×pow1
6×associate-*l*
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-*r/ fma-udef sin-mult
Counts
4 → 94
Calls
4 calls:
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
11.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
12.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
14.0ms
(* (sin a) (sin b))

series683.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
186.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
311.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
54.0ms
(* (sin a) (sin b))

simplify1.9s

Counts
106 → 106
Iterations

Useful iterations: done (1.9s)

IterNodesCost
015647980
137445387
2170345065
done500044970

prune904.0ms

Pruning

12 alts after pruning (11 fresh and 1 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 b) (sin a)))
0.2b
(* (sin b) (sin a))
0.3b
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

rewrite76.0ms

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)
23.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
9.0ms
(* (sin b) (sin a))
23.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series589.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin b) r)
128.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
70.0ms
(* (sin b) (sin a))
347.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify2.2s

Counts
98 → 98
Iterations

Useful iterations: 2 (455.0ms)

IterNodesCost
015535840
138533816
2184533121
done500033121

prune596.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes330.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
012458
118458
220458
done20458

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.0s2960×body1280valid
1.5s1897×body640valid
340.0ms707×body320valid
260.0ms2060×body80valid
184.0ms376×body160valid