Details

Time bar (total: 16.6s)

sample81.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
9.0ms276×body80nan

simplify51.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite52.0ms

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:
19.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
25.0ms
(/ (- 1.0 x) (+ 1.0 x))
2.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series165.0ms

Counts
3 → 9
Calls
3 calls:
106.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
40.0ms
(/ (- 1.0 x) (+ 1.0 x))
19.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify2.4s

Counts
100 → 100
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01671451
13561376
28651284
321471268
done50001252

prune291.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
95×*-un-lft-identity
66×add-sqr-sqrt
61×times-frac
52×sqrt-prod
37×add-cube-cbrt
30×log-pow
29×exp-prod
16×distribute-lft-out
13×distribute-lft-out-- difference-of-squares
6×pow1 add-exp-log associate-/r/ add-cbrt-cube
5×associate-/l*
4×associate-/r* add-log-exp
3×log-prod flip3-+ flip-+ div-inv
2×rem-sqrt-square associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp rem-log-exp clear-num flip--
Counts
4 → 132
Calls
4 calls:
39.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
34.0ms
(/ (- 1.0 x) (+ 1.0 x))
1.0ms
(atan (log (exp (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
76.0ms
(log (exp (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

series340.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
56.0ms
(/ (- 1.0 x) (+ 1.0 x))
5.0ms
(atan (log (exp (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
142.0ms
(log (exp (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

simplify1.8s

Counts
144 → 144
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02222096
14151874
29251735
322241706
done50001680

prune632.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (exp (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))))
0.0b
(atan (log (exp (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))))
0.0b
(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
0.0b
(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
183×*-un-lft-identity
156×sqrt-prod
128×cbrt-prod
123×add-sqr-sqrt
120×times-frac
87×unpow-prod-down cube-prod
75×add-cube-cbrt
68×log-pow
67×exp-prod
30×distribute-lft-out
24×distribute-lft-out-- difference-of-squares
12×associate-/r/
7×pow1
6×flip3-+ flip-+ div-inv
5×add-exp-log add-cbrt-cube
4×add-log-exp
3×cube-mult pow-unpow log-prod pow-pow unpow3 sqr-pow
2×cube-div sqrt-div
1×pow-to-exp cbrt-div sqrt-pow1 pow1/2 pow1/3 rem-log-exp pow-exp sqrt-pow2 rem-cbrt-cube rem-cube-cbrt
Counts
4 → 239
Calls
4 calls:
176.0ms
(log (exp (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))))
1.0ms
(atan (log (exp (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))))
25.0ms
(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
34.0ms
(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

series536.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(log (exp (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))))
3.0ms
(atan (log (exp (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))))
120.0ms
(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
273.0ms
(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

simplify3.8s

Counts
251 → 251
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
03234972
16853624
213133437
347633383
done50013383

prune645.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
0.0b
(cbrt (+ 1.0 x))
0.0b
(cbrt (+ 1.0 x))
0.0b
(cbrt (+ 1.0 x))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
60.0ms
(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
4.0ms
(cbrt (+ 1.0 x))
11.0ms
(cbrt (+ 1.0 x))
4.0ms
(cbrt (+ 1.0 x))

series564.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
140.0ms
(cbrt (+ 1.0 x))
141.0ms
(cbrt (+ 1.0 x))
145.0ms
(cbrt (+ 1.0 x))

simplify1.9s

Counts
107 → 107
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01391485
13081358
27721288
318921148
done50011116

prune692.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes70.0ms

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
11313
done1313

end0.0ms

sample2.0s

Algorithm
intervals
Results
907.0ms7937×body80nan
655.0ms8000×body80valid