Details

Time bar (total: 6.6s)

sample275.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
7.0ms275×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0166
1196
2216
3216

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
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))

rewrite23.0ms

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))))
7.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms
(/ (- 1.0 x) (+ 1.0 x))

series150.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
93.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
54.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify38.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0354753
11071709
25001690

prune224.0ms

Filtered
100 candidates to 70 candidates (70.0%)
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 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
0.0b
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
0.0b
(/ 1 (sqrt (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
144×*-un-lft-identity
134×times-frac
84×sqrt-prod
72×add-cube-cbrt
41×associate-*r*
32×add-exp-log
27×associate-*l*
20×add-cbrt-cube
18×distribute-lft-out
15×distribute-lft-out-- difference-of-squares unswap-sqr
14×associate-/r*
11×pow1 sqrt-div div-exp
8×prod-exp associate-/r/ associate-/l*
6×cbrt-undiv
4×flip3-+ cbrt-unprod flip-+ div-inv add-log-exp
3×rec-exp pow-flip sqrt-pow1 1-exp
2×frac-times frac-2neg pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num associate-/l/
1×flip3-- div-sub *-commutative flip-- inv-pow
Counts
4 → 236
Calls
4 calls:
18.0ms
(sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
32.0ms
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
7.0ms
(/ 1 (sqrt (+ 1.0 x)))
9.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
35.0ms
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
51.0ms
(/ 1 (sqrt (+ 1.0 x)))
92.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify93.0ms

Algorithm
egg-herbie
Counts
248 → 248
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
08072327
138032038
250011912

prune465.0ms

Filtered
248 candidates to 129 candidates (52.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
1051×*-un-lft-identity
967×times-frac
654×sqrt-prod
557×add-sqr-sqrt
498×associate-*l*
325×add-cube-cbrt
271×distribute-lft-out
164×unpow-prod-down cube-prod
92×distribute-lft-out-- difference-of-squares
41×sqrt-div sum-cubes
28×associate-/r/
18×flip3-+ flip-+
15×add-exp-log add-cbrt-cube
14×div-inv unswap-sqr
9×pow1
7×associate-/r*
6×associate-*r*
5×associate-/l*
4×cbrt-undiv frac-times associate-*r/ div-exp add-log-exp
3×prod-exp cbrt-unprod
2×sqrt-pow1 pow-prod-down associate-*l/ associate-/l/
1×flip3-- frac-2neg pow1/2 div-sub clear-num *-commutative flip--
Counts
4 → 625
Calls
4 calls:
1.0ms
(atan (sqrt (* (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ (pow 1.0 3) (pow x 3)))) (sqrt (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))))
110.0ms
(* (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ (pow 1.0 3) (pow x 3)))) (sqrt (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
54.0ms
(sqrt (* (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ (pow 1.0 3) (pow x 3)))) (sqrt (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
9.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series538.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(atan (sqrt (* (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ (pow 1.0 3) (pow x 3)))) (sqrt (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))))
134.0ms
(* (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ (pow 1.0 3) (pow x 3)))) (sqrt (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
299.0ms
(sqrt (* (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ (pow 1.0 3) (pow x 3)))) (sqrt (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
92.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify175.0ms

Algorithm
egg-herbie
Counts
637 → 637
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
0132210833
1440910641
2500210615

prune1.6s

Filtered
637 candidates to 272 candidates (42.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
99×sqrt-prod
84×add-sqr-sqrt
80×times-frac
70×cbrt-prod
56×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
10×associate-/r*
9×distribute-lft-out
8×cbrt-div associate-/l*
6×add-exp-log
5×add-cbrt-cube
4×pow1 flip3-- sqrt-div flip-- add-log-exp
3×pow1/3
2×associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv
Counts
4 → 159
Calls
4 calls:
3.0ms
(cbrt (- 1.0 x))
3.0ms
(cbrt (- 1.0 x))
3.0ms
(cbrt (- 1.0 x))
11.0ms
(/ (cbrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x))))

series514.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(cbrt (- 1.0 x))
98.0ms
(cbrt (- 1.0 x))
94.0ms
(cbrt (- 1.0 x))
230.0ms
(/ (cbrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x))))

simplify53.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04871965
113091894
250011786

prune961.0ms

Filtered
171 candidates to 109 candidates (63.7%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes23.0ms

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
02919
12919

end0.0ms

sample719.0ms

Algorithm
intervals
Results
311.0ms8000×body80valid
205.0ms8017×body80nan