Details

Time bar (total: 5.1s)

analyze665.0ms

Algorithm
search

sample59.0ms

Algorithm
intervals
Results
25.0ms66×body1280valid
13.0ms54×body640valid
5.0ms33×body320valid
4.0ms88×body80valid
2.0ms15×body160valid

simplify473.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1287
2407
3737
41767
55597
626267
750017

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.8b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.9b
(- (exp (* 2.0 x)) 1.0)
4.9b
(- (exp x) 1.0)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
75×*-un-lft-identity
51×times-frac
31×sqrt-prod
27×add-cube-cbrt
24×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-/r* flip-- associate-/l*
4×associate-/r/
2×sub-neg rem-sqrt-square diff-log div-inv associate-/l/
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num
Counts
4 → 123
Calls
4 calls:
8.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.0ms
(- (exp (* 2.0 x)) 1.0)
6.0ms
(- (exp x) 1.0)

series31.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
7.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.0ms
(- (exp (* 2.0 x)) 1.0)
10.0ms
(- (exp x) 1.0)

simplify130.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
03871380
110541314
242651301
350011293

prune237.0ms

Filtered
92 candidates to 135 candidates (-46.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1323135
Fresh000
Picked101
Done000
Total1333136

Merged error: 0.0b

Counts
136 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (+ 1.0 (* 0.5 x)))
9.1b
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube
3×associate-*r* associate-*l* sqrt-prod
2×flip3-+ sqrt-div associate-*r/ flip-+ add-log-exp
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 37
Calls
2 calls:
5.0ms
(* x (+ 1.0 (* 0.5 x)))
5.0ms
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series11.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(* x (+ 1.0 (* 0.5 x)))
5.0ms
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify38.0ms

Algorithm
egg-herbie
Counts
43 → 43
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0279280
11132268
25002256

prune60.0ms

Filtered
30 candidates to 43 candidates (-43.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New43043
Fresh022
Picked011
Done000
Total43346

Merged error: 0.0b

Counts
46 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
0.2b
(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.2b
(/ (pow x 2) (sqrt 2.0))
0.4b
(/ x (sqrt 2.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
108×add-sqr-sqrt
83×*-un-lft-identity
81×add-cube-cbrt
67×sqrt-prod
52×associate-*l*
41×unpow-prod-down
21×add-exp-log
15×unpow2 sqr-pow
13×add-cbrt-cube
12×associate-/r*
11×associate-/l*
9×add-log-exp unswap-sqr
7×div-exp
6×pow1 associate-*r*
4×associate-*r/ prod-exp
3×cbrt-undiv sum-log div-inv
2×distribute-rgt-in frac-times pow-to-exp sub-neg flip3-- frac-2neg distribute-lft-in flip3-+ frac-add pow-exp clear-num flip-- cbrt-unprod flip-+ difference-of-squares
1×+-commutative associate-+r+ pow-prod-down associate-*l/ *-commutative distribute-lft-out--
Counts
4 → 221
Calls
4 calls:
9.0ms
(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
20.0ms
(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
6.0ms
(/ (pow x 2) (sqrt 2.0))
4.0ms
(/ x (sqrt 2.0))

series31.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
13.0ms
(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
6.0ms
(/ (pow x 2) (sqrt 2.0))
5.0ms
(/ x (sqrt 2.0))

simplify88.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07231889
130421708
250011694

prune477.0ms

Filtered
143 candidates to 233 candidates (-62.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2321233
Fresh011
Picked101
Done011
Total2333236

Merged error: 0b

Counts
236 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow x 2) (sqrt 2.0))
0.4b
(/ x (sqrt 2.0))
0.7b
(pow (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))) 3)
7.0b
(cbrt (pow (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))) 3))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
57×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
39×sqrt-prod
27×unpow-prod-down
12×add-exp-log cbrt-prod associate-/r*
11×associate-/l*
9×add-cbrt-cube sqr-pow
8×cube-div
7×unpow2
6×cube-prod
5×pow1
4×cbrt-div flip3-+ associate-*r/ div-exp frac-add flip-+ add-log-exp
3×pow-unpow
2×cbrt-undiv cube-mult pow-to-exp frac-2neg unpow3 pow-exp clear-num div-inv
1×pow-pow pow1/3 rem-cbrt-cube rem-cube-cbrt
Counts
4 → 167
Calls
4 calls:
6.0ms
(/ (pow x 2) (sqrt 2.0))
4.0ms
(/ x (sqrt 2.0))
9.0ms
(pow (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))) 3)
9.0ms
(cbrt (pow (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))) 3))

series29.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ (pow x 2) (sqrt 2.0))
5.0ms
(/ x (sqrt 2.0))
12.0ms
(pow (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))) 3)
7.0ms
(cbrt (pow (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))) 3))

simplify89.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06432097
128341893
250011874

prune406.0ms

Filtered
101 candidates to 179 candidates (-77.2%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1790179
Fresh011
Picked011
Done011
Total1793182

Merged error: 0b

Counts
182 → 3

regimes39.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.3b

bsearch22.0ms

Steps
ItersRangePoint
8
-0.009543975034899833
-7.196642984029448e-07
-8.497431105885146e-05

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03020
13020

end0.0ms

analyze459.0ms

Algorithm
search

sample1.6s

Algorithm
intervals
Results
808.0ms2220×body1280valid
378.0ms1653×body640valid
129.0ms845×body320valid
129.0ms2874×body80valid
40.0ms408×body160valid
0.0ms4×body80invalid

Profiling

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