Details

Time bar (total: 9.3s)

sample291.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
7.0ms272×body80nan

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (+ 1.0 x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
45×add-sqr-sqrt
41×times-frac
26×sqrt-prod
24×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
5×add-exp-log add-cbrt-cube associate-/l*
4×pow1 associate-/r* associate-/r/
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
3 → 97
Calls
3 calls:
0.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
14.0ms
(/ (- 1.0 x) (+ 1.0 x))

series150.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
94.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
52.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify2.0s

Counts
106 → 106
Iterations

Useful iterations: 3 (588.0ms)

IterNodesCost
01731505
13681422
29801333
347851320
done50001320

prune233.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan (sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))))
0.0b
(/ x (+ 1.0 x))
0.0b
(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))
0.0b
(/ 1.0 (+ 1.0 x))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
582×*-un-lft-identity
484×times-frac
332×add-sqr-sqrt
324×prod-diff
320×add-cube-cbrt
123×distribute-lft-out
82×associate-/r/
41×flip3-+ flip-+ div-inv
18×fma-neg
8×add-exp-log associate-/r* add-cbrt-cube
7×distribute-lft-out--
6×associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u difference-of-squares
3×distribute-rgt-out--
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 451
Calls
4 calls:
0.0ms
(atan (sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))))
5.0ms
(/ x (+ 1.0 x))
60.0ms
(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))
5.0ms
(/ 1.0 (+ 1.0 x))

series130.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan (sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))))
39.0ms
(/ x (+ 1.0 x))
63.0ms
(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))
25.0ms
(/ 1.0 (+ 1.0 x))

simplify862.0ms

Counts
463 → 463
Iterations

Useful iterations: done (833.0ms)

IterNodesCost
046420714
198218208
2251113632
done500113578

prune756.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ 1.0 x))
0.0b
(- (/ 1.0 (+ 1.0 x)) (log (exp (/ x (+ 1.0 x)))))
0.0b
(/ 1.0 (+ 1.0 x))
6.6b
(log (exp (/ x (+ 1.0 x))))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
649×*-un-lft-identity
529×times-frac
396×prod-diff
383×add-sqr-sqrt
378×add-cube-cbrt
362×log-pow
342×exp-prod
134×distribute-lft-out
88×associate-/r/
44×flip3-+ flip-+ div-inv
24×pow1
18×fma-neg
8×add-exp-log associate-/r* add-cbrt-cube
6×log-prod associate-/l*
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate--r+
2×cbrt-undiv frac-2neg div-exp clear-num distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- diff-log rem-log-exp flip--
Counts
4 → 537
Calls
4 calls:
5.0ms
(/ x (+ 1.0 x))
94.0ms
(- (/ 1.0 (+ 1.0 x)) (log (exp (/ x (+ 1.0 x)))))
5.0ms
(/ 1.0 (+ 1.0 x))
11.0ms
(log (exp (/ x (+ 1.0 x))))

series155.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ x (+ 1.0 x))
60.0ms
(- (/ 1.0 (+ 1.0 x)) (log (exp (/ x (+ 1.0 x)))))
24.0ms
(/ 1.0 (+ 1.0 x))
33.0ms
(log (exp (/ x (+ 1.0 x))))

simplify871.0ms

Counts
549 → 549
Iterations

Useful iterations: done (845.0ms)

IterNodesCost
054427223
1104420587
2253015628
done500015606

prune821.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (- x 1.0))
0.0b
(* x (- x 1.0))
0.0b
(* (- (/ x (+ (pow 1.0 3) (pow x 3)))) (fma 1.0 1.0 (* x (- x 1.0))))
0.0b
(fma (/ 1.0 (- (* 1.0 1.0) (* x x))) (- 1.0 x) (* (- (/ x (+ (pow 1.0 3) (pow x 3)))) (fma 1.0 1.0 (* x (- x 1.0)))))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
124×*-un-lft-identity
76×associate-*l*
70×add-sqr-sqrt
60×add-cube-cbrt
54×times-frac
36×prod-diff
33×distribute-lft-neg-in distribute-rgt-neg-in
30×distribute-lft-out
24×unpow-prod-down cube-prod
23×distribute-rgt-in distribute-lft-in
13×associate-*r*
10×pow1 add-exp-log add-cbrt-cube
6×sum-cubes
4×expm1-log1p-u sub-neg associate-*r/ associate-/r/ log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
2×flip3-- flip3-+ flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
1×distribute-lft-neg-out neg-mul-1 associate-*l/ distribute-neg-frac
Counts
4 → 193
Calls
4 calls:
11.0ms
(* x (- x 1.0))
11.0ms
(* x (- x 1.0))
122.0ms
(* (- (/ x (+ (pow 1.0 3) (pow x 3)))) (fma 1.0 1.0 (* x (- x 1.0))))
0.0ms
(fma (/ 1.0 (- (* 1.0 1.0) (* x x))) (- 1.0 x) (* (- (/ x (+ (pow 1.0 3) (pow x 3)))) (fma 1.0 1.0 (* x (- x 1.0)))))

series268.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* x (- x 1.0))
43.0ms
(* x (- x 1.0))
74.0ms
(* (- (/ x (+ (pow 1.0 3) (pow x 3)))) (fma 1.0 1.0 (* x (- x 1.0))))
107.0ms
(fma (/ 1.0 (- (* 1.0 1.0) (* x x))) (- 1.0 x) (* (- (/ x (+ (pow 1.0 3) (pow x 3)))) (fma 1.0 1.0 (* x (- x 1.0)))))

simplify764.0ms

Counts
205 → 205
Iterations

Useful iterations: 2 (238.0ms)

IterNodesCost
02423819
15343426
220173025
done50003025

prune760.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01217
11417
done1417

end0.0ms

sample708.0ms

Algorithm
intervals
Results
308.0ms8000×body80valid
208.0ms8067×body80nan