Details

Time bar (total: 5.0s)

sample83.0ms

Algorithm
intervals
Results
32.0ms87×body2560valid
20.0ms90×body1280valid
7.0ms263×body80nan
6.0ms34×body640valid
3.0ms22×body320valid
1.0ms15×body160valid
0.0ms8×body80valid

simplify101.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0207
1437
2847
31557
42627
54547
628787
750017
done50017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

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))
0.7b
(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:
26.0ms
(/ (- 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)))

series111.0ms

Counts
3 → 9
Calls
3 calls:
80.0ms
(/ (- 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)))

simplify40.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0349623
11288567
25001565
done5001565

prune176.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b
(* 5.0 (* v v))
0.7b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
57×*-un-lft-identity
55×add-cube-cbrt
49×times-frac
39×prod-diff
13×fma-neg
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp difference-of-squares
5×div-inv
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod associate-/l*
2×asin-acos associate-/r/ associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num *-commutative distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 139
Calls
4 calls:
26.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
22.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
16.0ms
(* 5.0 (* v v))
1.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series143.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
32.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
25.0ms
(* 5.0 (* v v))
4.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify71.0ms

Counts
151 → 151
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05762948
119411851
250031839
done50031839

prune317.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.0b
(expm1 (log1p (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
0.2b
(* 5.0 (* v v))
0.7b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
6×add-sqr-sqrt
5×expm1-log1p-u add-cube-cbrt *-un-lft-identity
4×log1p-expm1-u add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
1×asin-acos log1p-udef expm1-log1p log1p-expm1 associate-*r* *-commutative expm1-udef unswap-sqr
Counts
4 → 53
Calls
4 calls:
1.0ms
(log1p (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.0ms
(expm1 (log1p (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
16.0ms
(* 5.0 (* v v))
1.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(log1p (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
244.0ms
(expm1 (log1p (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
26.0ms
(* 5.0 (* v v))
4.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify125.0ms

Counts
65 → 65
Iterations

Useful iterations: 4 (119.0ms)

IterNodesCost
0170557
1449482
21165479
33864478
45001473
done5001473

prune180.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.2b
(* 5.0 (* v v))
0.2b
(* 5.0 (* v v))
0.7b
(asin (* (* (cbrt (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (cbrt (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×associate-*l* pow-prod-down prod-exp cbrt-unprod
7×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* *-commutative unswap-sqr
1×asin-acos
Counts
4 → 73
Calls
4 calls:
18.0ms
(* 5.0 (* v v))
16.0ms
(* 5.0 (* v v))
17.0ms
(* 5.0 (* v v))
1.0ms
(asin (* (* (cbrt (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (cbrt (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series85.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* 5.0 (* v v))
25.0ms
(* 5.0 (* v v))
25.0ms
(* 5.0 (* v v))
6.0ms
(asin (* (* (cbrt (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (cbrt (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify114.0ms

Counts
85 → 85
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
0128589
1355495
2962495
33288478
45001478
done5001478

prune209.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

regimes88.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01826
11826
done1826

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s2966×body2560valid
577.0ms2543×body1280valid
228.0ms8270×body80nan
202.0ms1258×body640valid
73.0ms618×body320valid
31.0ms383×body160valid
11.0ms232×body80valid