Details

Time bar (total: 7.0s)

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize4.0ms

Local error

Found 1 expressions with local error:

16.8b
(/ 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))

simplify56.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0171215
1589196
21979191
35002186

prune67.0ms

Filtered
34 candidates to 29 candidates (85.3%)
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)))
16.8b
(sqrt (+ (* x x) 1.0))
16.8b
(sqrt (+ (* x x) 1.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
30×sqrt-prod
12×associate-/r*
10×add-exp-log
8×pow1 sqrt-div add-cbrt-cube
6×associate-/l*
4×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u add-log-exp
3×pow-flip sqrt-pow1 pow1/2 div-exp
2×cbrt-undiv rem-sqrt-square frac-2neg clear-num hypot-def div-inv
1×rec-exp 1-exp inv-pow
Counts
4 → 128
Calls
4 calls:
7.0ms
(/ x (sqrt (+ (* x x) 1.0)))
7.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
4.0ms
(sqrt (+ (* x x) 1.0))
4.0ms
(sqrt (+ (* x x) 1.0))

series275.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ x (sqrt (+ (* x x) 1.0)))
72.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
45.0ms
(sqrt (+ (* x x) 1.0))
41.0ms
(sqrt (+ (* x x) 1.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0409999
11612916
25001867

prune271.0ms

Filtered
140 candidates to 97 candidates (69.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

2.8b
(/ x (fma (- 1.0) 1.0 (pow x 4)))
20.9b
(* (/ x (fma (- 1.0) 1.0 (pow x 4))) (- (* x x) 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
19×times-frac
13×associate-*l*
9×add-exp-log add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×pow1 associate-*r*
3×associate-/r* associate-/l*
2×cbrt-undiv expm1-log1p-u frac-times sub-neg flip3-- associate-*r/ div-exp prod-exp flip-- cbrt-unprod log1p-expm1-u div-inv add-log-exp unswap-sqr
1×frac-2neg pow-prod-down associate-*l/ clear-num *-commutative difference-of-squares
Counts
2 → 78
Calls
2 calls:
2.0ms
(/ x (fma (- 1.0) 1.0 (pow x 4)))
18.0ms
(* (/ x (fma (- 1.0) 1.0 (pow x 4))) (- (* x x) 1.0))

series264.0ms

Counts
2 → 6
Calls
2 calls:
153.0ms
(/ x (fma (- 1.0) 1.0 (pow x 4)))
111.0ms
(* (/ x (fma (- 1.0) 1.0 (pow x 4))) (- (* x x) 1.0))

simplify60.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0446816
12125716
25001706

prune179.0ms

Filtered
84 candidates to 62 candidates (73.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite620.0ms

Algorithm
rewrite-expression-head
Rules
3607×times-frac
2350×add-sqr-sqrt
2310×*-un-lft-identity
2288×add-cube-cbrt
2000×prod-diff
1212×unpow-prod-down
1002×associate-+r+
466×cube-prod
410×sqr-pow
154×cube-mult unpow3
138×div-inv
25×fma-neg
20×difference-of-squares
19×associate-/r*
14×add-exp-log
13×fma-def
11×add-log-exp
8×add-cbrt-cube distribute-lft-out--
6×div-exp associate-/l*
5×distribute-lft-out
4×pow1 expm1-log1p-u log1p-expm1-u
3×frac-add
2×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log pow-exp clear-num sum-log frac-sub flip--
1×+-commutative associate-+r- flip3-+ flip-+
Counts
4 → 2217
Calls
4 calls:
255.0ms
(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
4.0ms
(/ 1.0 (pow x 3))
3.0ms
(/ 1.0 (pow x 5))
92.0ms
(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
35.0ms
(/ 1.0 (pow x 3))
49.0ms
(/ 1.0 (pow x 5))
122.0ms
(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

simplify476.0ms

Algorithm
egg-herbie
Counts
2229 → 2229
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0409048855
1500242336

prune4.0s

Filtered
2229 candidates to 903 candidates (40.5%)
Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes21.0ms

Accuracy

100% (0.0b remaining)

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

bsearch52.0ms

Steps
ItersRangePoint
9
4717.815806685034
26105877676.696735
7670.359014713688
6
-4707863282.998968
-1117730599.3323822
-2100410095.8698003

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03314
13314

end0.0ms

sample214.0ms

Algorithm
intervals
Results
134.0ms8000×body80valid