Details

Time bar (total: 4.3s)

sample290.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
13.0ms242×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0166
1196
2216
3216

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
23×add-sqr-sqrt
20×times-frac
13×add-cube-cbrt
6×distribute-lft-out
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log associate-/r* add-cbrt-cube
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp clear-num flip-- flip-+ div-inv
Counts
2 → 57
Calls
2 calls:
14.0ms
(/ (- 1.0 x) (+ 1.0 x))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series53.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(/ (- 1.0 x) (+ 1.0 x))
9.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify98.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 3 (91.0ms)

IterNodesCost
0242403
1723377
23210375
35001372

prune148.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
136×add-sqr-sqrt
123×*-un-lft-identity
113×times-frac
71×sqrt-prod
57×add-cube-cbrt
41×associate-*r*
28×add-exp-log
27×associate-*l*
18×add-cbrt-cube
15×distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
9×div-exp
8×sqrt-div prod-exp
7×pow1 associate-/r*
6×associate-/r/
5×cbrt-undiv associate-/l*
4×expm1-log1p-u flip3-+ cbrt-unprod flip-+ log1p-expm1-u add-log-exp
3×div-inv
2×rec-exp 1-exp associate-/l/
1×frac-times rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative flip-- hypot-def
Counts
4 → 203
Calls
4 calls:
4.0ms
(sqrt (+ 1.0 x))
13.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
59.0ms
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
0.0ms
(atan (sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))

series162.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ 1.0 x))
93.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
36.0ms
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
3.0ms
(atan (sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))

simplify85.0ms

Algorithm
egg-herbie
Counts
215 → 215
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07202079
131281804
250021702

prune464.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
173×*-un-lft-identity
167×cbrt-prod
142×times-frac
139×add-sqr-sqrt
81×sqrt-prod
77×add-cube-cbrt
44×associate-*r*
28×distribute-lft-out-- difference-of-squares
23×pow1
20×distribute-lft-out
15×cbrt-div
12×pow1/3
9×add-exp-log pow-prod-up
8×sqrt-div associate-/r/
6×pow-plus
5×frac-times pow-prod-down associate-*l/ add-cbrt-cube
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u div-inv add-log-exp unswap-sqr
3×associate-*r/ prod-exp pow-sqr cbrt-unprod
2×pow2
1×associate-*l* pow3 *-commutative
Counts
4 → 240
Calls
4 calls:
7.0ms
(cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
7.0ms
(cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
7.0ms
(cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
105.0ms
(* (* (cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))) (cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))) (cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))

series777.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
228.0ms
(cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
225.0ms
(cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
92.0ms
(* (* (cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))) (cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))) (cbrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))

simplify88.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06553493
121993265
250023090

prune730.0ms

Pruning

2 alts after pruning (0 fresh and 2 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

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01811
11811

end0.0ms

sample1.1s

Algorithm
intervals
Results
516.0ms8000×body80valid
375.0ms8027×body80nan