Details

Time bar (total: 3.3s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms98×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune2.0ms

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: 0.2b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
2×flip3-+ associate-/r/ flip-+
1×+-commutative frac-2neg clear-num div-inv
Counts
2 → 8
Calls
2 calls:
2.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series180.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(+ 1.0 (sqrt (+ x 1.0)))
140.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify98.0ms

Algorithm
egg-herbie
Counts
14 → 14
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0193127
1699110
2400098
3500196

prune43.0ms

Filtered
14 candidates to 12 candidates (85.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New11314
Fresh000
Picked101
Done000
Total12315

Merged error: 0b

Counts
15 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sqrt (+ x 1.0)) 3)
0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.8b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.0b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-div
31×flip3-+ flip-+
28×associate-*r/
16×frac-sub
12×frac-times
10×*-commutative
8×associate-*l/
7×pow1/2
4×prod-diff sub-div
2×distribute-rgt-out-- fma-neg associate-/r/ distribute-lft-out--
1×pow2 pow-to-exp sub-neg flip3-- pow-pow frac-2neg sqrt-unprod unpow3 pow-prod-down clear-num associate-/r* rem-square-sqrt pow-sqr sum-cubes pow-prod-up sqrt-pow2 flip-- div-inv sqr-pow
Counts
4 → 60
Calls
4 calls:
2.0ms
(pow (sqrt (+ x 1.0)) 3)
5.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
10.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(pow (sqrt (+ x 1.0)) 3)
16.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
65.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
189.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify52.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0558946
11896772
25001758

prune201.0ms

Filtered
72 candidates to 44 candidates (61.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New72072
Fresh022
Picked011
Done000
Total72375

Merged error: 0b

Counts
75 → 3

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 1/4 (/ (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) 1.0) (/ x (+ (sqrt 1.0) 1.0)))
0.0b
(fma (/ 1/8 (* (pow (+ (sqrt 1.0) 1.0) 2) 1.0)) (/ (pow x 3) (sqrt 1.0)) (fma 1/4 (/ (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) 1.0) (/ x (+ (sqrt 1.0) 1.0))))
8.4b
(fma (- (/ 1/2 (pow (+ (sqrt 1.0) 1.0) 2))) (/ (pow x 2) (sqrt 1.0)) (fma (/ 1/8 (* (pow (+ (sqrt 1.0) 1.0) 2) 1.0)) (/ (pow x 3) (sqrt 1.0)) (fma 1/4 (/ (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) 1.0) (/ x (+ (sqrt 1.0) 1.0)))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
3×fma-udef
Counts
3 → 3
Calls
3 calls:
1.0ms
(fma 1/4 (/ (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) 1.0) (/ x (+ (sqrt 1.0) 1.0)))
4.0ms
(fma (/ 1/8 (* (pow (+ (sqrt 1.0) 1.0) 2) 1.0)) (/ (pow x 3) (sqrt 1.0)) (fma 1/4 (/ (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) 1.0) (/ x (+ (sqrt 1.0) 1.0))))
1.0ms
(fma (- (/ 1/2 (pow (+ (sqrt 1.0) 1.0) 2))) (/ (pow x 2) (sqrt 1.0)) (fma (/ 1/8 (* (pow (+ (sqrt 1.0) 1.0) 2) 1.0)) (/ (pow x 3) (sqrt 1.0)) (fma 1/4 (/ (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) 1.0) (/ x (+ (sqrt 1.0) 1.0)))))

series1.5s

Counts
3 → 9
Calls
3 calls:
330.0ms
(fma 1/4 (/ (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) 1.0) (/ x (+ (sqrt 1.0) 1.0)))
734.0ms
(fma (/ 1/8 (* (pow (+ (sqrt 1.0) 1.0) 2) 1.0)) (/ (pow x 3) (sqrt 1.0)) (fma 1/4 (/ (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) 1.0) (/ x (+ (sqrt 1.0) 1.0))))
429.0ms
(fma (- (/ 1/2 (pow (+ (sqrt 1.0) 1.0) 2))) (/ (pow x 2) (sqrt 1.0)) (fma (/ 1/8 (* (pow (+ (sqrt 1.0) 1.0) 2) 1.0)) (/ (pow x 3) (sqrt 1.0)) (fma 1/4 (/ (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) 1.0) (/ x (+ (sqrt 1.0) 1.0)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
12 → 12
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
094190
1376187
21930181
35002180

prune37.0ms

Filtered
12 candidates to 6 candidates (50.0%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New12012
Fresh011
Picked011
Done011
Total12315

Merged error: 0b

Counts
15 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
3.9b
(- 1.0 (sqrt (+ x 1.0)))
4.0b
(- (- (* 1.0 1.0) x) 1.0)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
7×flip3-- flip--
6×frac-times
5×sub-neg
3×frac-2neg associate-*l* associate-*l/ clear-num
2×distribute-rgt-in distribute-lft-in associate-*r/ associate--l+ associate-/r/
1×associate--l- *-commutative div-inv
Counts
3 → 30
Calls
3 calls:
8.0ms
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
2.0ms
(- 1.0 (sqrt (+ x 1.0)))
5.0ms
(- (- (* 1.0 1.0) x) 1.0)

series138.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
53.0ms
(- 1.0 (sqrt (+ x 1.0)))
12.0ms
(- (- (* 1.0 1.0) x) 1.0)

simplify37.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0263317
11236304
25002288

prune73.0ms

Filtered
39 candidates to 29 candidates (74.4%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New39039
Fresh000
Picked011
Done022
Total39342

Merged error: 0b

Counts
42 → 3

regimes24.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 7.0b

bsearch37.0ms

Steps
ItersRangePoint
9
2.5653698016906928e-06
357.20278190505735
1.3911727598234371

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02926
12926

end0.0ms

sample323.0ms

Algorithm
intervals
Results
163.0ms7999×body80valid
44.0ms2627×body80nan
0.0ms1×body1280valid