Details

Time bar (total: 14.5s)

sample88.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
11.0ms276×body80nan

simplify74.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))))

rewrite91.0ms

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:
32.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
47.0ms
(/ (- 1.0 x) (+ 1.0 x))
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series217.0ms

Counts
3 → 9
Calls
3 calls:
138.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
53.0ms
(/ (- 1.0 x) (+ 1.0 x))
25.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01671451
13561376
28651284
321471268
done50001252

prune334.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize29.0ms

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)))))

rewrite170.0ms

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:
23.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
49.0ms
(/ (- 1.0 x) (+ 1.0 x))
2.0ms
(atan (log (exp (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
87.0ms
(log (exp (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
59.0ms
(/ (- 1.0 x) (+ 1.0 x))
5.0ms
(atan (log (exp (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
147.0ms
(log (exp (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

simplify1.9s

Counts
144 → 144
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02222096
14151874
29251735
322241706
done50001680

prune486.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

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)

rewrite260.0ms

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:
157.0ms
(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)))))
43.0ms
(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
40.0ms
(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

series546.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(log (exp (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))))
6.0ms
(atan (log (exp (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))))
111.0ms
(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
285.0ms
(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

simplify3.9s

Counts
251 → 251
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
03234972
16853624
213133437
347633383
done50013383

prune674.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

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:
85.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
9.0ms
(cbrt (+ x 1.0))
9.0ms
(cbrt (+ x 1.0))
10.0ms
(cbrt (+ x 1.0))

series523.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
137.0ms
(cbrt (+ x 1.0))
121.0ms
(cbrt (+ x 1.0))
136.0ms
(cbrt (+ x 1.0))

simplify2.1s

Counts
107 → 107
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01391485
13081358
27721288
318921148
done50001116

prune676.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes2.0ms