Details

Time bar (total: 3.3s)

sample10.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073
173

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize4.0ms

Local error

Found 1 expressions with local error:

17.6b
(/ x (+ (* x x) 1.0))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg flip3-+ div-exp clear-num flip-+ log1p-expm1-u div-inv add-log-exp
Counts
1 → 31
Calls
1 calls:
6.0ms
(/ x (+ (* x x) 1.0))

series57.0ms

Counts
1 → 3
Calls
1 calls:
57.0ms
(/ x (+ (* x x) 1.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0171215
1589196
21979191
35002186

prune72.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* x x) 1.0)))
0.0b
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
17.6b
(sqrt (+ (* x x) 1.0))
17.6b
(sqrt (+ (* x x) 1.0))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 168
Calls
4 calls:
9.0ms
(/ x (sqrt (+ (* x x) 1.0)))
42.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))
5.0ms
(sqrt (+ (* x x) 1.0))

series265.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(/ x (sqrt (+ (* x x) 1.0)))
53.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
47.0ms
(sqrt (+ (* x x) 1.0))
41.0ms
(sqrt (+ (* x x) 1.0))

simplify78.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06341778
129781575
250011440

prune351.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* x x) 1.0)))
0.0b
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
17.6b
(sqrt (+ (* x x) 1.0))
17.6b
(sqrt (+ (* x x) 1.0))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 168
Calls
4 calls:
6.0ms
(/ x (sqrt (+ (* x x) 1.0)))
45.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))
4.0ms
(sqrt (+ (* x x) 1.0))

series264.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ x (sqrt (+ (* x x) 1.0)))
58.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))
41.0ms
(sqrt (+ (* x x) 1.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06341778
129781575
250011440

prune380.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

5.1b
(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
15.0b
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
17.6b
(sqrt (+ (* x x) 1.0))
21.0b
(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
9×add-log-exp
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×associate-+r+ associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log associate-/r/ hypot-def
1×cbrt-undiv +-commutative associate-+r- sub-neg sqrt-undiv hypot-udef fma-def frac-2neg diff-log div-exp prod-diff clear-num div-inv
Counts
4 → 99
Calls
4 calls:
34.0ms
(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
17.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
4.0ms
(sqrt (+ (* x x) 1.0))
32.0ms
(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

series411.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
44.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
41.0ms
(sqrt (+ (* x x) 1.0))
248.0ms
(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

simplify55.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04211546
115701415
250011380

prune417.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.3b

bsearch255.0ms

Steps
ItersRangePoint
9
251.47950061764826
104248118811.33417
7097.135133098112
8
-4.877250012809174e+31
-1.2788576461633362e+29
-1.0191567175789878e+31

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04628
14628

end0.0ms

sample239.0ms

Algorithm
intervals
Results
148.0ms8000×body80valid