Details

Time bar (total: 24.9s)

sample136.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
26.0ms274×body80nan

simplify74.0ms

Counts
1 → 1
Iterations
IterNodes
421
321
219
116
09

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
79×*-un-lft-identity
56×add-sqr-sqrt
49×times-frac
30×sqrt-prod
26×add-cube-cbrt
18×difference-of-squares
13×distribute-lft-out
9×distribute-lft-out--
6×associate-/l*
5×add-cbrt-cube add-exp-log
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 clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub div-exp flip--
Counts
3 → 106
Calls
3 calls:
21.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
31.0ms
(/ (- 1 x) (+ 1 x))
3.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series128.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
42.0ms
(/ (- 1 x) (+ 1 x))
17.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify1.7s

Counts
115 → 115
Iterations
IterNodes
32078
2729
1338
0171

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1 x) (+ 1 x))
0.0b
(atan (sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x))))))
0.0b
(log1p (/ (- 1 x) (+ 1 x)))
0.0b
(expm1 (log1p (/ (- 1 x) (+ 1 x))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
31×add-sqr-sqrt
24×times-frac
16×add-cube-cbrt
10×difference-of-squares
7×distribute-lft-out
6×add-cbrt-cube add-exp-log associate-/l*
5×expm1-log1p-u distribute-lft-out--
4×pow1 associate-/r* log1p-expm1-u add-log-exp
2×associate-/r/ associate-/l/
1×cbrt-undiv log1p-udef expm1-log1p clear-num frac-2neg flip3-+ flip3-- div-sub div-exp log1p-expm1 flip-+ div-inv flip-- expm1-udef
Counts
4 → 84
Calls
4 calls:
24.0ms
(/ (- 1 x) (+ 1 x))
1.0ms
(atan (sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x))))))
1.0ms
(log1p (/ (- 1 x) (+ 1 x)))
1.0ms
(expm1 (log1p (/ (- 1 x) (+ 1 x))))

series199.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (- 1 x) (+ 1 x))
2.0ms
(atan (sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x))))))
77.0ms
(log1p (/ (- 1 x) (+ 1 x)))
90.0ms
(expm1 (log1p (/ (- 1 x) (+ 1 x))))

simplify2.0s

Counts
96 → 96
Iterations
IterNodes
32666
2894
1368
0165

prune945.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (log (sqrt (/ (- 1 x) (+ 1 x)))))
0.0b
(/ (- 1 x) (+ 1 x))
0.0b
(atan (exp (log (sqrt (/ (- 1 x) (+ 1 x))))))
5.3b
(log (sqrt (/ (- 1 x) (+ 1 x))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
80×add-sqr-sqrt
72×times-frac
66×log-prod
60×sqrt-prod
41×add-cube-cbrt
33×exp-sum
26×difference-of-squares
19×distribute-lft-out
13×distribute-lft-out--
8×pow1
7×add-exp-log
6×exp-prod add-cbrt-cube associate-/r/ log-pow associate-/l*
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×flip3-+ flip-+ div-inv
2×log-div sqrt-pow1 pow1/2 sqrt-div associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- exp-diff div-sub div-exp rem-log-exp flip-- rem-exp-log
Counts
4 → 159
Calls
4 calls:
18.0ms
(exp (log (sqrt (/ (- 1 x) (+ 1 x)))))
15.0ms
(/ (- 1 x) (+ 1 x))
1.0ms
(atan (exp (log (sqrt (/ (- 1 x) (+ 1 x))))))
6.0ms
(log (sqrt (/ (- 1 x) (+ 1 x))))

series239.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(exp (log (sqrt (/ (- 1 x) (+ 1 x)))))
38.0ms
(/ (- 1 x) (+ 1 x))
4.0ms
(atan (exp (log (sqrt (/ (- 1 x) (+ 1 x))))))
136.0ms
(log (sqrt (/ (- 1 x) (+ 1 x))))

simplify2.0s

Counts
171 → 171
Iterations
IterNodes
32503
2939
1490
0285

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1 x) (+ 1 x))
0.0b
(atan (sqrt (expm1 (log (+ 1 (/ (- 1 x) (+ 1 x)))))))
0.0b
(expm1 (log (+ 1 (/ (- 1 x) (+ 1 x)))))
0.0b
(log (+ 1 (/ (- 1 x) (+ 1 x))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
32×add-sqr-sqrt
24×times-frac
17×add-cube-cbrt
10×difference-of-squares
8×distribute-lft-out
7×add-exp-log
6×add-cbrt-cube associate-/l*
5×pow1 log1p-expm1-u distribute-lft-out--
4×expm1-log1p-u log-prod associate-/r* add-log-exp
2×log-div expm1-log1p log1p-def flip3-+ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp rem-log-exp log-pow div-inv flip-- expm1-udef
Counts
4 → 92
Calls
4 calls:
16.0ms
(/ (- 1 x) (+ 1 x))
1.0ms
(atan (sqrt (expm1 (log (+ 1 (/ (- 1 x) (+ 1 x)))))))
1.0ms
(expm1 (log (+ 1 (/ (- 1 x) (+ 1 x)))))
32.0ms
(log (+ 1 (/ (- 1 x) (+ 1 x))))

series240.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ (- 1 x) (+ 1 x))
3.0ms
(atan (sqrt (expm1 (log (+ 1 (/ (- 1 x) (+ 1 x)))))))
137.0ms
(expm1 (log (+ 1 (/ (- 1 x) (+ 1 x)))))
76.0ms
(log (+ 1 (/ (- 1 x) (+ 1 x))))

simplify10.2s

Counts
104 → 104
Iterations
IterNodes
32998
2994
1407
0187

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes115.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
213
113
011

end0.0ms

sample2.1s

Algorithm
intervals
Results
930.0ms8000×body80valid
833.0ms8249×body80nan