Details

Time bar (total: 16.2s)

sample84.0ms

Algorithm
intervals
Results
35.0ms96×body2560valid
18.0ms81×body1280valid
7.0ms238×body80nan
6.0ms34×body640valid
2.0ms21×body320valid
2.0ms18×body160valid
0.0ms6×body80valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
12014
24314
38414
415514
524114
633014
748214
8110714
done500114

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b
(* 5.0 (* v v))
0.6b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×times-frac
10×add-exp-log add-cbrt-cube
8×pow1
4×associate-/r* difference-of-squares
3×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u associate-/l* add-log-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv acos-asin frac-2neg div-sub div-exp associate-*r* clear-num *-commutative div-inv unswap-sqr
Counts
3 → 69
Calls
3 calls:
24.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
18.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series112.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
26.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.5s

Counts
78 → 78
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01451268
13351223
210141120
333001118
done50011116

prune188.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* 5.0 (* v v)) 3)
0.2b
(* 5.0 (* v v))
0.2b
(* 5.0 (* v v))
0.6b
(acos (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (* (- (pow v 2) 1.0) (fma (* 5.0 (* v v)) (fma (* v v) 5.0 1.0) (* 1.0 1.0)))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt pow-prod-down prod-exp cbrt-unprod
7×add-cube-cbrt *-un-lft-identity
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow pow-pow pow-exp rem-cube-cbrt
2×associate-*r* *-commutative unswap-sqr
1×acos-asin cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod sqr-pow
Counts
4 → 79
Calls
4 calls:
15.0ms
(pow (* 5.0 (* v v)) 3)
16.0ms
(* 5.0 (* v v))
19.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (* (- (pow v 2) 1.0) (fma (* 5.0 (* v v)) (fma (* v v) 5.0 1.0) (* 1.0 1.0)))))

series119.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(pow (* 5.0 (* v v)) 3)
27.0ms
(* 5.0 (* v v))
29.0ms
(* 5.0 (* v v))
10.0ms
(acos (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (* (- (pow v 2) 1.0) (fma (* 5.0 (* v v)) (fma (* v v) 5.0 1.0) (* 1.0 1.0)))))

simplify725.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
0941126
11981024
2779938
done5001938

prune294.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (fma v v (pow v 4)) 4.0)
0.6b
(acos (- (* (fma v v (pow v 4)) 4.0) 1.0))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×associate-*r* associate-*l*
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×acos-asin pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 30
Calls
2 calls:
7.0ms
(* (fma v v (pow v 4)) 4.0)
1.0ms
(acos (- (* (fma v v (pow v 4)) 4.0) 1.0))

series109.0ms

Counts
2 → 6
Calls
2 calls:
105.0ms
(* (fma v v (pow v 4)) 4.0)
3.0ms
(acos (- (* (fma v v (pow v 4)) 4.0) 1.0))

simplify2.3s

Counts
36 → 36
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
058451
1104439
2317379
31305379
done5001379

prune83.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0)))
1.0b
(cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0)))
1.0b
(cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0)))
1.0b
(* (cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0))) (cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
1.0ms
(cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0)))
1.0ms
(cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0)))
1.0ms
(cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0)))
11.0ms
(* (cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0))) (cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0))))

series526.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0)))
123.0ms
(cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0)))
124.0ms
(cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0)))
152.0ms
(* (cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0))) (cbrt (acos (- (* (fma v v (pow v 4)) 4.0) 1.0))))

simplify3.6s

Counts
93 → 93
Iterations

Useful iterations: done (3.6s)

IterNodesCost
0622150
11091985
22881633
39771550
442381525
done50001462

prune203.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes24.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01834
12034
done2034

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s3000×body2560valid
560.0ms2486×body1280valid
222.0ms7918×body80nan
202.0ms1230×body640valid
80.0ms654×body320valid
34.0ms412×body160valid
11.0ms218×body80valid