Details

Time bar (total: 14.2s)

sample346.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
7.0ms238×body80nan

simplify17.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune34.0ms

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))

rewrite45.0ms

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×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 → 91
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
16.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
23.0ms
(/ (- 1.0 x) (+ 1.0 x))

series139.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
87.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
48.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify1.2s

Counts
100 → 100
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01671451
13561376
28661284
321471268
done50011252

prune218.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
0.0b
(/ (+ 1.0 x) (- 1.0 x))
0.0b
(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
0.0b
(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
322×times-frac
289×*-un-lft-identity
214×add-sqr-sqrt
139×add-cube-cbrt
83×sqrt-prod
41×distribute-lft-out
33×distribute-lft-out-- difference-of-squares
31×associate-/r*
18×associate-/r/
17×add-exp-log
11×add-cbrt-cube
10×div-inv
8×flip3-- div-exp flip--
7×pow1 associate-/l*
5×rem-sqrt-square
4×cbrt-undiv add-log-exp
3×sqrt-pow1
2×rec-exp pow-flip frac-2neg 1-exp clear-num associate-/l/ inv-pow
1×flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 280
Calls
4 calls:
1.0ms
(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
25.0ms
(/ (+ 1.0 x) (- 1.0 x))
26.0ms
(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
26.0ms
(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

series159.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
34.0ms
(/ (+ 1.0 x) (- 1.0 x))
89.0ms
(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
33.0ms
(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

simplify1.9s

Counts
292 → 292
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03685447
16984596
215184100
339273860
done50013830

prune365.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan (sqrt (* (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0))))))
0.0b
(/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0)))
0.0b
(sqrt (* (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0)))))
0.0b
(* (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0))))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
141×*-un-lft-identity
125×times-frac
106×associate-*l*
64×difference-of-squares
49×add-cube-cbrt
48×unpow-prod-down cube-prod
32×sqr-pow
30×add-exp-log
25×distribute-lft-out
20×distribute-lft-out--
18×add-cbrt-cube
15×associate-*r*
10×pow1 div-exp
8×prod-exp
6×associate-/r/ unswap-sqr
5×cbrt-undiv
4×difference-cubes sqrt-div cbrt-unprod add-log-exp
3×rec-exp flip3-+ 1-exp associate-/r* flip-+ div-inv associate-/l*
2×frac-times sqrt-pow1 associate-*r/ pow-prod-down associate-*l/ un-div-inv
1×pow-flip frac-2neg pow1/2 clear-num sqrt-prod *-commutative inv-pow
Counts
4 → 207
Calls
4 calls:
1.0ms
(atan (sqrt (* (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0))))))
22.0ms
(/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0)))
38.0ms
(sqrt (* (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0)))))
165.0ms
(* (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0))))

series261.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(atan (sqrt (* (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0))))))
52.0ms
(/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0)))
129.0ms
(sqrt (* (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0)))))
73.0ms
(* (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0))))

simplify1.1s

Counts
219 → 219
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03075593
19135229
225834683
done50014681

prune511.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite794.0ms

Algorithm
rewrite-expression-head
Rules
3811×times-frac
3052×add-sqr-sqrt
2932×*-un-lft-identity
1620×sqrt-prod
1566×unpow-prod-down cube-prod
1222×add-cube-cbrt
1216×difference-of-squares
660×cbrt-prod
610×sqr-pow
475×distribute-lft-out
380×distribute-lft-out--
106×associate-/l*
76×difference-cubes
50×associate-/r/
25×flip3-+ flip-+ div-inv
10×add-exp-log add-cbrt-cube
7×pow1
4×add-log-exp
3×cbrt-undiv rem-sqrt-square pow-unpow pow-pow sqrt-div div-exp associate-/r*
2×cube-div cube-mult sqrt-pow1 pow1/2 unpow3 div-sub
1×pow-to-exp cbrt-div frac-2neg pow1/3 pow-exp clear-num sqrt-pow2 rem-cbrt-cube associate-/l/ rem-cube-cbrt
Counts
4 → 2127
Calls
4 calls:
101.0ms
(sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (+ (* x (+ x 1.0)) (* 1.0 1.0))))
162.0ms
(cbrt (pow (sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (+ (* x (+ x 1.0)) (* 1.0 1.0)))) 3))
100.0ms
(/ (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (+ (* x (+ x 1.0)) (* 1.0 1.0)))
138.0ms
(pow (sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (+ (* x (+ x 1.0)) (* 1.0 1.0)))) 3)

series555.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (+ (* x (+ x 1.0)) (* 1.0 1.0))))
134.0ms
(cbrt (pow (sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (+ (* x (+ x 1.0)) (* 1.0 1.0)))) 3))
67.0ms
(/ (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (+ (* x (+ x 1.0)) (* 1.0 1.0)))
226.0ms
(pow (sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (+ 1.0 x)) (+ (* x (+ x 1.0)) (* 1.0 1.0)))) 3)

simplify1.7s

Counts
2139 → 2139
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01457107864
1369196959
done500096429

prune3.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes19.0ms

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
01113
11513
done1513

end0.0ms

sample758.0ms

Algorithm
intervals
Results
301.0ms8000×body80valid
201.0ms7910×body80nan