Details

Time bar (total: 18.6s)

sample45.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
14.0ms283×body80nan

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (7.0ms)

IterNodesCost
01416
12116
22516
32915
43215
53315
done3315

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))
0.9b
(/ (acos (/ (- g) h)) 3.0)
1.0b
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×div-sub fma-udef
1×cbrt-undiv acos-neg acos-asin cos-sum frac-2neg distribute-frac-neg div-exp clear-num div-inv
Counts
3 → 51
Calls
3 calls:
0.0ms
(fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))
3.0ms
(/ (acos (/ (- g) h)) 3.0)
1.0ms
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

series141.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))
11.0ms
(/ (acos (/ (- g) h)) 3.0)
99.0ms
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

simplify2.0s

Counts
60 → 60
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0103842
1153818
2272740
3587740
41253740
53089740
done5000740

prune192.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (acos (/ (- g) h)) (sqrt 3.0))
0.9b
(* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))
1.0b
(cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))
1.0b
(/ 1 (sqrt 3.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
106×add-sqr-sqrt
94×times-frac
66×*-un-lft-identity
60×add-cube-cbrt
53×sqrt-prod
32×add-exp-log
22×associate-*r* associate-*l*
20×add-cbrt-cube
15×unswap-sqr
12×associate-/r*
11×div-exp
8×pow1 prod-exp
6×cbrt-undiv associate-/l*
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp pow-flip 1-exp
2×frac-2neg div-sub clear-num
1×acos-neg acos-asin frac-times cos-sum sqrt-pow1 pow1/2 associate-*r/ distribute-frac-neg pow-prod-down associate-*l/ *-commutative fma-udef inv-pow
Counts
4 → 185
Calls
4 calls:
4.0ms
(/ (acos (/ (- g) h)) (sqrt 3.0))
25.0ms
(* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))
1.0ms
(cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))
3.0ms
(/ 1 (sqrt 3.0))

series362.0ms

Counts
4 → 10
Calls
4 calls:
42.0ms
(/ (acos (/ (- g) h)) (sqrt 3.0))
85.0ms
(* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))
234.0ms
(cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))
0.0ms
(/ 1 (sqrt 3.0))

simplify4.3s

Counts
195 → 195
Iterations

Useful iterations: 3 (3.0s)

IterNodesCost
02203077
15012742
213582278
342482212
done50012212

prune494.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b
(expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))))
0.9b
(/ (acos (/ (- g) h)) 3.0)
1.0b
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))
1.0b
(log1p (expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
5×log1p-expm1-u
4×pow1 expm1-log1p-u add-log-exp
3×associate-/r* associate-/l*
2×div-sub
1×cbrt-undiv acos-neg acos-asin cos-sum log1p-udef expm1-log1p frac-2neg log1p-expm1 distribute-frac-neg div-exp clear-num fma-udef div-inv expm1-udef
Counts
4 → 63
Calls
4 calls:
0.0ms
(expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))))
3.0ms
(/ (acos (/ (- g) h)) 3.0)
1.0ms
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))
0.0ms
(log1p (expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))))
11.0ms
(/ (acos (/ (- g) h)) 3.0)
105.0ms
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))
176.0ms
(log1p (expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))))

simplify3.7s

Counts
75 → 75
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
01151134
11701072
2276964
3509964
4847964
51264964
62467964
done5000964

prune242.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b
(expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))))
0.9b
(/ (acos (/ (- g) h)) 3.0)
1.0b
(+ 1 (expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))))
1.0b
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt add-cube-cbrt
9×times-frac
6×add-exp-log add-cbrt-cube add-log-exp
5×log1p-expm1-u
4×pow1 expm1-log1p-u
3×fma-def associate-/r* associate-/l*
2×div-sub expm1-udef
1×cbrt-undiv acos-neg +-commutative acos-asin associate-+r- cos-sum expm1-log1p frac-2neg flip3-+ distribute-frac-neg div-exp clear-num sum-log flip-+ fma-udef div-inv distribute-lft-out
Counts
4 → 70
Calls
4 calls:
0.0ms
(expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))))
3.0ms
(/ (acos (/ (- g) h)) 3.0)
3.0ms
(+ 1 (expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))))
1.0ms
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))))
11.0ms
(/ (acos (/ (- g) h)) 3.0)
146.0ms
(+ 1 (expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))))
100.0ms
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

simplify4.6s

Counts
82 → 82
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
01281302
12211210
23951101
37991101
416201101
534021101
done50011101

prune273.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes149.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02051
12551
done2551

end0.0ms

sample1.2s

Algorithm
intervals
Results
494.0ms8000×body80valid
405.0ms8100×body80nan