Details

Time bar (total: 8.5s)

sample317.0ms

Algorithm
intervals
Results
43.0ms99×body1280valid
16.0ms64×body640valid
4.0ms24×body320valid
3.0ms59×body80valid
1.0ms10×body160valid

simplify17.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
089
1129
2159
3199
4209
done209

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (/ (sin b) (cos (+ a b))))
0.2b
(/ (sin b) (cos (+ a b)))
3.3b
(cos (+ a b))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*r*
10×add-exp-log add-cbrt-cube
5×pow1
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
3 → 73
Calls
3 calls:
9.0ms
(* r (/ (sin b) (cos (+ a b))))
4.0ms
(/ (sin b) (cos (+ a b)))
6.0ms
(cos (+ a b))

series157.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(* r (/ (sin b) (cos (+ a b))))
37.0ms
(/ (sin b) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify490.0ms

Counts
82 → 82
Iterations

Useful iterations: done (487.0ms)

IterNodesCost
0122955
1269924
21033834
done5000831

prune218.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
20×associate-*r*
19×times-frac
13×add-exp-log add-cbrt-cube
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×flip3-- prod-exp associate-/r* frac-sub flip-- cbrt-unprod associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×sub-neg frac-2neg fma-neg diff-log associate-*r/ prod-diff clear-num
Counts
4 → 110
Calls
4 calls:
5.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
24.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms
(* (sin a) (sin b))
9.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series455.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
215.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms
(* (sin a) (sin b))
110.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify645.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (157.0ms)

IterNodesCost
01812200
14402141
217201949
done50001949

prune422.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin b) (sin a))
0.2b
(/ (sin b) (/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin a) (sin b)))))
0.3b
(* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
0.3b
(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin a) (sin b))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
30×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
22×add-exp-log add-cbrt-cube
10×associate-/r*
8×pow1
7×cbrt-undiv div-exp
6×associate-*r* associate-*l* div-inv
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u associate-/l* add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative fma-udef unswap-sqr
1×distribute-rgt-in distribute-lft-in associate-/r/ sin-mult
Counts
4 → 116
Calls
4 calls:
4.0ms
(* (sin b) (sin a))
5.0ms
(/ (sin b) (/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin a) (sin b)))))
3.0ms
(* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
4.0ms
(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin a) (sin b))))

series421.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (sin b) (sin a))
114.0ms
(/ (sin b) (/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin a) (sin b)))))
171.0ms
(* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
88.0ms
(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin a) (sin b))))

simplify1.0s

Counts
128 → 128
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01994617
14714573
224242780
done50002768

prune518.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
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×times-frac prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×sub-neg frac-2neg fma-neg diff-log prod-diff clear-num div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
3.0ms
(* r (sin b))
5.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
4.0ms
(* (sin a) (sin b))
11.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series385.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* r (sin b))
84.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
50.0ms
(* (sin a) (sin b))
214.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify526.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (123.0ms)

IterNodesCost
01521364
13751324
214671174
done50011174

prune319.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01638
12238
22438
done2438

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2963×body1280valid
464.0ms1882×body640valid
138.0ms733×body320valid
109.0ms2086×body80valid
41.0ms339×body160valid