Details

Time bar (total: 2.7s)

sample9.0ms

Algorithm
intervals
Results
4.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073
173

prune1.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.0b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

15.0b
(/ x (+ (* x x) 1.0))

rewrite6.0ms

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:
5.0ms
(/ x (+ (* x x) 1.0))

series57.0ms

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

simplify57.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0171215
1589196
21979191
35002186

prune62.0ms

Filtered
34 candidates to 29 candidates (85.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New30434
Fresh000
Picked101
Done000
Total31435

Merged error: 0b

Counts
35 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (+ (* x x) 1.0)))
0.0b
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
15.0b
(sqrt (+ (* x x) 1.0))
15.0b
(sqrt (+ (* x x) 1.0))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
30×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×pow1 sqrt-div div-exp
8×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×rec-exp pow-flip sqrt-pow1 pow1/2 1-exp div-inv associate-/l*
2×rem-sqrt-square hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
4 → 174
Calls
4 calls:
7.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
28.0ms
(* (/ 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))

series212.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
56.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
44.0ms
(sqrt (+ (* x x) 1.0))
43.0ms
(sqrt (+ (* x x) 1.0))

simplify81.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06441789
132241573
250011402

prune258.0ms

Filtered
186 candidates to 117 candidates (62.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1860186
Fresh033
Picked011
Done000
Total1864190

Merged error: 0b

Counts
190 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ 1 (fma x x 1.0))
14.7b
(* x (/ 1 (fma x x 1.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×times-frac
19×*-un-lft-identity
18×add-cube-cbrt
15×add-exp-log
13×associate-*r*
9×add-cbrt-cube
5×pow1
4×div-exp prod-exp
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv expm1-log1p-u rec-exp 1-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
2 → 71
Calls
2 calls:
3.0ms
(/ 1 (fma x x 1.0))
7.0ms
(* x (/ 1 (fma x x 1.0)))

series110.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(/ 1 (fma x x 1.0))
65.0ms
(* x (/ 1 (fma x x 1.0)))

simplify39.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0278377
11193324
25001294

prune86.0ms

Filtered
77 candidates to 47 candidates (61.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New77077
Fresh022
Picked011
Done011
Total77481

Merged error: 0b

Counts
81 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
0.1b
(/ 1 (pow x 3))
0.2b
(/ 1 (pow x 5))
18.9b
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
1934×times-frac
1320×add-sqr-sqrt
1236×*-un-lft-identity
1171×add-cube-cbrt
1000×prod-diff
650×unpow-prod-down
251×cube-prod
238×sqr-pow
79×cube-mult unpow3
72×div-inv
63×difference-of-squares
25×fma-neg
22×add-exp-log
19×associate-/r*
12×div-exp
8×add-cbrt-cube
7×distribute-lft-out--
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv pow-flip frac-2neg clear-num inv-pow
1×sub-neg flip3-- diff-log frac-sub flip-- fma-udef
Counts
4 → 1250
Calls
4 calls:
1.0ms
(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
6.0ms
(/ 1 (pow x 3))
5.0ms
(/ 1 (pow x 5))
72.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
30.0ms
(/ 1 (pow x 3))
41.0ms
(/ 1 (pow x 5))
97.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify287.0ms

Algorithm
egg-herbie
Counts
1262 → 1262
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
0241131677
1500218869

prune644.0ms

Filtered
1262 candidates to 195 candidates (15.5%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New126201262
Fresh011
Picked011
Done022
Total126241266

Merged error: 0b

Counts
1266 → 4

regimes24.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch58.0ms

Steps
ItersRangePoint
9
137964.03928948785
661184882896.0549
7485940.540660984
8
-9.00906372646185e+157
-2.4392292464634512e+153
-1.324933943149559e+154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03116
13116

end0.0ms

sample210.0ms

Algorithm
intervals
Results
131.0ms8000×body80valid