Details

Time bar (total: 11.2s)

sample45.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
13.0ms275×body80nan

simplify36.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (13.0ms)

IterNodesCost
01416
12116
22516
32915
43215
53315
done3315

prune6.0ms

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

rewrite11.0ms

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))
6.0ms
(/ (acos (/ (- g) h)) 3.0)
3.0ms
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

series153.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))
12.0ms
(/ (acos (/ (- g) h)) 3.0)
103.0ms
(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

simplify2.1s

Counts
60 → 60
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0103842
1153818
2275740
3538740
41224740
53602740
done5000740

prune387.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
91×add-sqr-sqrt
76×times-frac
51×*-un-lft-identity
45×add-cube-cbrt
41×sqrt-prod
30×add-exp-log
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×div-exp
8×pow1 prod-exp
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×rec-exp pow-flip 1-exp div-inv associate-/l*
2×fma-udef
1×frac-times cos-sum frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
4 → 152
Calls
4 calls:
0.0ms
(fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0))))
2.0ms
(cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))
43.0ms
(* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))
7.0ms
(/ 1 (sqrt 3.0))

series388.0ms

Counts
4 → 10
Calls
4 calls:
100.0ms
(fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0))))
209.0ms
(cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))
79.0ms
(* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))
0.0ms
(/ 1 (sqrt 3.0))

simplify2.3s

Counts
162 → 162
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02002682
14582288
212341838
335521742
done50001730

prune395.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
1.0b
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
1.0b
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
1.0b
(* (cbrt (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))) (cbrt (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×add-cube-cbrt *-un-lft-identity
11×pow1
6×add-exp-log pow1/3 swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
3×cos-sum fma-udef
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 72
Calls
4 calls:
2.0ms
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
2.0ms
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
2.0ms
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
14.0ms
(* (cbrt (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))) (cbrt (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))))

series534.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
106.0ms
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
104.0ms
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
221.0ms
(* (cbrt (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))) (cbrt (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))))

simplify1.2s

Counts
84 → 84
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0792237
11302064
22581872
34831576
410581560
done50001515

prune287.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b
(fma 0.3333333333333333 (acos (- (/ g h))) (* 0.6666666666666666 PI))
1.0b
(cbrt (pow (cos (fma 0.3333333333333333 (acos (- (/ g h))) (* 0.6666666666666666 PI))) 2))
1.0b
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
1.0b
(cos (fma 0.3333333333333333 (acos (- (/ g h))) (* 0.6666666666666666 PI)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×unpow-prod-down fma-udef
2×cos-sum
1×pow1/3 unpow2 sqr-pow
Counts
4 → 48
Calls
4 calls:
0.0ms
(fma 0.3333333333333333 (acos (- (/ g h))) (* 0.6666666666666666 PI))
3.0ms
(cbrt (pow (cos (fma 0.3333333333333333 (acos (- (/ g h))) (* 0.6666666666666666 PI))) 2))
2.0ms
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
3.0ms
(cos (fma 0.3333333333333333 (acos (- (/ g h))) (* 0.6666666666666666 PI)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(fma 0.3333333333333333 (acos (- (/ g h))) (* 0.6666666666666666 PI))
224.0ms
(cbrt (pow (cos (fma 0.3333333333333333 (acos (- (/ g h))) (* 0.6666666666666666 PI))) 2))
103.0ms
(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))
104.0ms
(cos (fma 0.3333333333333333 (acos (- (/ g h))) (* 0.6666666666666666 PI)))

simplify1.0s

Counts
60 → 60
Iterations

Useful iterations: 4 (373.0ms)

IterNodesCost
01001081
11411023
2236907
3519904
41949903
done5001903

prune294.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes217.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02833
13133
done3133

end0.0ms

sample1.2s

Algorithm
intervals
Results
457.0ms8000×body80valid
381.0ms8035×body80nan