Details

Time bar (total: 4.5s)

sample333.0ms

Algorithm
intervals
Results
37.0ms188×body10240exit
11.0ms371×body80nan
7.0ms233×body80valid
2.0ms23×body160valid

simplify72.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1287
2417
3757
41827
55767
626577
750017

prune4.0ms

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: 4.4b

Counts
2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.5b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.6b
(- (exp (* 2.0 x)) 1.0)
4.6b
(- (exp x) 1.0)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
6×flip3-- flip--
5×sqrt-div
4×associate-/r/ associate-/l/
3×sqrt-prod
2×sub-neg frac-2neg clear-num div-inv
1×pow1/2 div-sub
Counts
4 → 25
Calls
4 calls:
5.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms
(- (exp (* 2.0 x)) 1.0)
5.0ms
(- (exp x) 1.0)

series200.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms
(- (exp (* 2.0 x)) 1.0)
22.0ms
(- (exp x) 1.0)

simplify50.0ms

Algorithm
egg-herbie
Counts
37 → 37
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0214267
1556263
21769256
35002254

prune103.0ms

Filtered
37 candidates to 27 candidates (73.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New34337
Fresh000
Picked101
Done000
Total35338

Merged error: 0.5b

Counts
38 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.5b
(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
4.6b
(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b
(- (exp (* 2.0 x)) 1.0)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
7×associate-/r/
3×frac-2neg clear-num associate-/r* div-inv
2×flip3-- flip3-+ flip-- flip-+ associate-/l/
1×sub-neg div-sub fma-udef
Counts
4 → 22
Calls
4 calls:
7.0ms
(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
3.0ms
(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
1.0ms
(fma (- 1.0) 1.0 (exp (+ x x)))
4.0ms
(- (exp (* 2.0 x)) 1.0)

series250.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
67.0ms
(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
46.0ms
(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms
(- (exp (* 2.0 x)) 1.0)

simplify75.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0209259
1627255
22659230
35001230

prune108.0ms

Filtered
34 candidates to 26 candidates (76.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New33134
Fresh112
Picked011
Done000
Total34337

Merged error: 0.5b

Counts
37 → 3

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3)))
4.6b
(- (exp (* 2.0 x)) 1.0)
4.6b
(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b
(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×*-commutative
4×prod-diff
2×sub-neg flip3-- distribute-rgt-out-- fma-neg associate-/r/ flip-- distribute-lft-out--
1×frac-2neg flip3-+ clear-num associate-/r* sum-cubes flip-+ fma-udef div-inv
Counts
4 → 25
Calls
4 calls:
9.0ms
(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3)))
3.0ms
(- (exp (* 2.0 x)) 1.0)
1.0ms
(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms
(- (* 1.0 1.0) (* (exp x) 1.0))

series193.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3)))
30.0ms
(- (exp (* 2.0 x)) 1.0)
39.0ms
(fma (- 1.0) 1.0 (exp (+ x x)))
30.0ms
(- (* 1.0 1.0) (* (exp x) 1.0))

simplify70.0ms

Algorithm
egg-herbie
Counts
37 → 37
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0247225
1724214
22421210
35001194

prune127.0ms

Filtered
37 candidates to 23 candidates (62.2%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New37037
Fresh011
Picked011
Done011
Total37340

Merged error: 0.5b

Counts
40 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 0.5 (/ x (sqrt 2.0)) (sqrt 2.0))
0.2b
(fma (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)) (fma 0.5 (/ x (sqrt 2.0)) (sqrt 2.0)))
0.2b
(/ (pow x 2) (sqrt 2.0))
0.4b
(/ x (sqrt 2.0))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
2×frac-2neg clear-num fma-udef div-inv associate-/l*
1×unpow2 sqr-pow
Counts
4 → 10
Calls
4 calls:
1.0ms
(fma 0.5 (/ x (sqrt 2.0)) (sqrt 2.0))
1.0ms
(fma (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)) (fma 0.5 (/ x (sqrt 2.0)) (sqrt 2.0)))
3.0ms
(/ (pow x 2) (sqrt 2.0))
2.0ms
(/ x (sqrt 2.0))

series322.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(fma 0.5 (/ x (sqrt 2.0)) (sqrt 2.0))
90.0ms
(fma (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)) (fma 0.5 (/ x (sqrt 2.0)) (sqrt 2.0)))
62.0ms
(/ (pow x 2) (sqrt 2.0))
58.0ms
(/ x (sqrt 2.0))

simplify61.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
05883
113980
239880
3175780
4500280

prune35.0ms

Filtered
22 candidates to 11 candidates (50.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New20222
Fresh000
Picked101
Done022
Total21425

Merged error: 0.5b

Counts
25 → 4

regimes28.0ms

Accuracy

72.3% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch62.0ms

Steps
ItersRangePoint
9
-3.467235455981812e-13
-1.3593094929530412e-20
-1.1188714909134117e-13

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03623
14023
24023

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s6558×body10240exit
385.0ms12631×body80nan
244.0ms7417×body80valid
59.0ms710×body160valid