Details

Time bar (total: 16.9s)

sample138.0ms

Algorithm
intervals
Results
51.0ms92×body2560valid
32.0ms79×body1280valid
15.0ms51×body640valid
13.0ms248×body80nan
4.0ms15×body320valid
2.0ms11×body160valid
1.0ms8×body80valid

simplify685.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
12014
24314
38414
415514
525414
694414
done500014

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize12.0ms

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))
0.5b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac
10×add-cbrt-cube add-exp-log
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×acos-asin cbrt-undiv clear-num frac-2neg div-sub div-exp associate-*r* *-commutative div-inv unswap-sqr
Counts
3 → 69
Calls
3 calls:
25.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
35.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series175.0ms

Counts
3 → 9
Calls
3 calls:
129.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
41.0ms
(* 5.0 (* v v))
5.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.6s

Counts
78 → 78
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01451268
13731229
218321123
done50001118

prune386.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (acos (/ (- 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))
0.5b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
6×add-sqr-sqrt
5×expm1-log1p-u *-un-lft-identity add-cube-cbrt
4×log1p-expm1-u add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
1×acos-asin log1p-udef expm1-log1p associate-*r* log1p-expm1 *-commutative expm1-udef unswap-sqr
Counts
4 → 53
Calls
4 calls:
0.0ms
(log1p (acos (/ (- 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)))))
22.0ms
(* 5.0 (* v v))
2.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
215.0ms
(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
36.0ms
(* 5.0 (* v v))
5.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify568.0ms

Counts
65 → 65
Iterations

Useful iterations: done (565.0ms)

IterNodesCost
079934
1163905
2637787
done5000783

prune315.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))
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))
0.5b
(acos (* (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
37×times-frac
29×*-un-lft-identity add-cube-cbrt
27×associate-*l*
21×difference-of-squares
16×add-exp-log
13×add-cbrt-cube
11×unpow-prod-down associate-*r*
9×sqr-pow
6×pow1 associate-/r* unswap-sqr
5×prod-exp
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×flip3-- cbrt-unprod flip-- associate-/l*
2×frac-times cbrt-undiv flip3-+ div-exp associate-*r/ *-commutative flip-+ div-inv unpow2 associate-/l/
1×distribute-rgt-in acos-asin pow-to-exp clear-num frac-2neg distribute-lft-in div-sub pow-prod-down associate-*l/ pow-exp
Counts
4 → 136
Calls
4 calls:
23.0ms
(/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))
75.0ms
(* (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0))
18.0ms
(* 5.0 (pow v 2))
3.0ms
(acos (* (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))
186.0ms
(* (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0))
53.0ms
(* 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)))

simplify461.0ms

Counts
148 → 148
Iterations

Useful iterations: done (450.0ms)

IterNodesCost
02693197
18833015
done50002736

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (log1p (expm1 (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))))) (+ (* v v) 1.0))
0.0b
(log1p (expm1 (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))))
0.2b
(* 5.0 (pow v 2))
0.5b
(acos (* (log1p (expm1 (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))))) (+ (* v v) 1.0)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
11×associate-*r* add-exp-log
9×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube
6×pow1 associate-*l*
5×unswap-sqr
4×expm1-log1p-u unpow-prod-down prod-exp log1p-expm1-u add-log-exp
2×associate-*r/ *-commutative cbrt-unprod unpow2 sqr-pow
1×distribute-rgt-in acos-asin pow-to-exp log1p-udef distribute-lft-in flip3-+ pow-prod-down pow-exp log1p-expm1 flip-+
Counts
4 → 74
Calls
4 calls:
25.0ms
(* (log1p (expm1 (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))))) (+ (* v v) 1.0))
0.0ms
(log1p (expm1 (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))))
19.0ms
(* 5.0 (pow v 2))
3.0ms
(acos (* (log1p (expm1 (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))))) (+ (* v v) 1.0)))

series1.9s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (log1p (expm1 (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))))) (+ (* v v) 1.0))
688.0ms
(log1p (expm1 (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0)))))
54.0ms
(* 5.0 (pow v 2))
9.0ms
(acos (* (log1p (expm1 (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 4) (* 1.0 1.0))))) (+ (* v v) 1.0)))

simplify2.1s

Counts
86 → 86
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01531717
13811513
219831318
done50011317

prune482.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes293.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01824
12124
done2124

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.2s3033×body2560valid
1.5s2489×body1280valid
834.0ms7888×body80nan
443.0ms1254×body640valid
134.0ms586×body320valid
64.0ms413×body160valid
20.0ms225×body80valid