Details

Time bar (total: 20.0s)

sample170.0ms

Algorithm
intervals
Results
55.0ms84×body2560valid
40.0ms87×body1280valid
30.0ms48×body640valid
14.0ms230×body80nan
4.0ms16×body320valid
2.0ms12×body160valid
1.0ms9×body80valid

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
12014
24314
38414
415514
525214
693414
done500014

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize14.0ms

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))
0.8b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite91.0ms

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:
53.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
32.0ms
(* 5.0 (* v v))
2.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series166.0ms

Counts
3 → 9
Calls
3 calls:
116.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
42.0ms
(* 5.0 (* v v))
8.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.8s

Counts
78 → 78
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01451268
13681227
218131122
done50011118

prune286.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0))
0.2b
(* 5.0 (pow v 2))
0.8b
(acos (* (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×associate-*l*
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×add-exp-log
11×associate-*r*
10×add-cbrt-cube
9×difference-of-squares
7×unpow-prod-down
6×unswap-sqr
5×pow1 prod-exp sqr-pow
3×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
2×frac-times flip3-+ associate-*r/ associate-/r/ *-commutative flip-+ unpow2
1×cbrt-undiv distribute-rgt-in acos-asin pow-to-exp flip3-- distribute-lft-in div-exp pow-prod-down associate-*l/ pow-exp flip-- div-inv
Counts
3 → 90
Calls
3 calls:
104.0ms
(* (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0))
13.0ms
(* 5.0 (pow v 2))
13.0ms
(acos (* (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0)))

series232.0ms

Counts
3 → 9
Calls
3 calls:
192.0ms
(* (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0))
31.0ms
(* 5.0 (pow v 2))
9.0ms
(acos (* (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0)))

simplify2.6s

Counts
99 → 99
Iterations

Useful iterations: 2 (818.0ms)

IterNodesCost
02082001
16861868
235431657
done50001657

prune533.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma v v 1.0) (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))))
0.0b
(expm1 (log1p (acos (* (fma v v 1.0) (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))))))
0.2b
(* 5.0 (pow v 2))
0.8b
(acos (* (fma v v 1.0) (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
32×associate-*r*
19×times-frac
18×add-cube-cbrt *-un-lft-identity
14×add-exp-log
11×add-cbrt-cube
9×difference-of-squares
7×unpow-prod-down
6×pow1 associate-*l* unswap-sqr
5×prod-exp sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-unprod
2×associate-/r/ *-commutative unpow2
1×cbrt-undiv acos-asin pow-to-exp expm1-log1p flip3-- associate-*r/ div-exp pow-prod-down pow-exp flip-- div-inv expm1-udef
Counts
4 → 95
Calls
4 calls:
111.0ms
(* (fma v v 1.0) (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))))
0.0ms
(expm1 (log1p (acos (* (fma v v 1.0) (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))))))
13.0ms
(* 5.0 (pow v 2))
2.0ms
(acos (* (fma v v 1.0) (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))))

series472.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(* (fma v v 1.0) (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))))
227.0ms
(expm1 (log1p (acos (* (fma v v 1.0) (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))))))
41.0ms
(* 5.0 (pow v 2))
8.0ms
(acos (* (fma v v 1.0) (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))))

simplify2.4s

Counts
107 → 107
Iterations

Useful iterations: 2 (727.0ms)

IterNodesCost
02022139
14852060
229131802
done50011802

prune593.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
0.0b
(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
0.9b
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×expm1-log1p-u
3×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
1×acos-asin log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
3 → 32
Calls
3 calls:
1.0ms
(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
1.0ms
(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
1.0ms
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series365.0ms

Counts
3 → 9
Calls
3 calls:
132.0ms
(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
223.0ms
(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
10.0ms
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify3.1s

Counts
41 → 41
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
044616
165590
297516
3186516
4541516
53015516
done5000516

prune149.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

regimes19.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01328
done1328

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.4s2993×body2560valid
1.0s2517×body1280valid
758.0ms1213×body640valid
593.0ms8054×body80nan
241.0ms660×body320valid
58.0ms406×body160valid
51.0ms211×body80valid