Details

Time bar (total: 5.0s)

sample81.0ms

Algorithm
intervals
Results
30.0ms93×body2560valid
19.0ms87×body1280valid
9.0ms258×body80nan
5.0ms32×body640valid
3.0ms22×body320valid
1.0ms16×body160valid
0.0ms6×body80valid

simplify94.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0207
1437
2847
31557
42627
54547
628787
750017
done50017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

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))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite44.0ms

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:
26.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
15.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series109.0ms

Counts
3 → 9
Calls
3 calls:
80.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify38.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0349623
11288567
25001565
done5001565

prune165.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b
(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.2b
(* 5.0 (* v v))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp difference-of-squares
3×associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l*
2×flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv acos-asin expm1-log1p frac-2neg div-sub div-exp associate-*r* clear-num *-commutative div-inv expm1-udef unswap-sqr
Counts
4 → 80
Calls
4 calls:
23.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0ms
(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
16.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
127.0ms
(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
29.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify40.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0361749
11295678
25001676
done5001676

prune227.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (+ v (sqrt 1.0))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0))))
0.2b
(* 5.0 (* v v))
0.2b
(* 5.0 (* v v))
2.4b
(acos (* (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (+ v (sqrt 1.0))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0)))))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
72×times-frac
64×*-un-lft-identity
44×associate-*r*
42×sqrt-prod
40×add-cube-cbrt
36×associate-*l*
26×add-exp-log add-cbrt-cube
16×pow1
12×difference-of-squares
11×unswap-sqr
10×prod-exp cbrt-unprod
7×pow-prod-down
6×distribute-lft-out distribute-lft-out--
4×cbrt-undiv expm1-log1p-u div-exp associate-/r/ log1p-expm1-u add-log-exp
3×*-commutative
2×div-inv
1×acos-asin frac-times flip3-- flip3-+ associate-*r/ associate-*l/ flip-- flip-+
Counts
4 → 155
Calls
4 calls:
99.0ms
(* (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (+ v (sqrt 1.0))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0))))
15.0ms
(* 5.0 (* v v))
16.0ms
(* 5.0 (* v v))
1.0ms
(acos (* (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (+ v (sqrt 1.0))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0)))))

series269.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(* (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (+ v (sqrt 1.0))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0))))
27.0ms
(* 5.0 (* v v))
30.0ms
(* 5.0 (* v v))
12.0ms
(acos (* (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (+ v (sqrt 1.0))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0)))))

simplify88.0ms

Counts
167 → 167
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07082337
132732015
250011985
done50011985

prune369.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(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)))))
0.4b
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
1×acos-asin expm1-log1p fma-udef expm1-udef
Counts
3 → 31
Calls
3 calls:
0.0ms
(fma 4.0 (fma v v (pow v 4)) (- 1.0))
0.0ms
(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)))

series214.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(fma 4.0 (fma v v (pow v 4)) (- 1.0))
156.0ms
(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
7.0ms
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify169.0ms

Counts
40 → 40
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
070262
1177231
2677231
34408231
45001231
done5001231

prune110.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes64.0ms

Accuracy

0% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01716
11716
done1716

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s2970×body2560valid
555.0ms2508×body1280valid
221.0ms8062×body80nan
208.0ms1312×body640valid
71.0ms598×body320valid
34.0ms412×body160valid
10.0ms200×body80valid