Details

Time bar (total: 5.3s)

analyze680.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%62.5%12.5%4
25%56.2%18.8%5
28.1%50%21.9%6
29.7%46.9%23.5%7
30.5%45.3%24.3%8
30.8%44.9%24.3%9
31.2%44.5%24.3%10
31.3%44.3%24.4%11
31.4%44.3%24.4%12
31.4%44%24.5%13
31.5%43.8%24.8%14

sample61.0ms

Algorithm
intervals
Results
30.0ms80×body1280valid
11.0ms48×body640valid
6.0ms31×body320valid
4.0ms89×body80valid
1.0ms8×body160valid

simplify463.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1287
2407
3737
41767
55597
626267
750017

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.5b

Counts
2 → 1

localize12.0ms

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))
3.1b
(- (exp x) 1.0)
3.3b
(- (exp (* 2.0 x)) 1.0)

rewrite36.0ms

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:
9.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
9.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms
(- (exp x) 1.0)
7.0ms
(- (exp (* 2.0 x)) 1.0)

series31.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
2.0ms
(- (exp x) 1.0)
10.0ms
(- (exp (* 2.0 x)) 1.0)

simplify129.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
03871380
110541314
242651301
350021293

prune244.0ms

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

localize14.0ms

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)))))
0.1b
(* (/ (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))

rewrite57.0ms

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:
10.0ms
(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
22.0ms
(* (/ (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))

series25.0ms

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)))))
6.0ms
(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
6.0ms
(/ (pow x 2) (sqrt 2.0))
6.0ms
(/ x (sqrt 2.0))

simplify87.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07231889
130421708
250011694

prune495.0ms

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

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2330233
Fresh022
Picked011
Done000
Total2333236

Merged error: 0.0b

Counts
236 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
0.0b
(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
3.1b
(- (exp x) 1.0)
3.1b
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
25×sqrt-prod
24×*-un-lft-identity
10×difference-of-squares
9×associate-*r*
8×add-cube-cbrt add-log-exp
7×pow1
6×add-exp-log flip3-- add-cbrt-cube flip-- distribute-lft-out--
5×times-frac associate-*l*
4×frac-times sub-neg
3×flip3-+ flip-+
2×distribute-rgt-in distribute-lft-in diff-log associate-*r/ associate-*l/ associate-/r/ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 92
Calls
4 calls:
16.0ms
(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
16.0ms
(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
4.0ms
(- (exp x) 1.0)
7.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series48.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
13.0ms
(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
2.0ms
(- (exp x) 1.0)
5.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify71.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05491338
124671202
250021178

prune274.0ms

Filtered
74 candidates to 104 candidates (-40.5%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1031104
Fresh011
Picked011
Done011
Total1034107

Merged error: 0b

Counts
107 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (exp x) 1.0)
3.1b
(- (exp x) 1.0)
3.1b
(- (exp x) 1.0)
3.1b
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×*-un-lft-identity
12×add-log-exp
7×difference-of-squares
6×sqrt-prod
5×distribute-lft-out--
4×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip--
Counts
4 → 60
Calls
4 calls:
4.0ms
(- (exp x) 1.0)
4.0ms
(- (exp x) 1.0)
4.0ms
(- (exp x) 1.0)
7.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series11.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(- (exp x) 1.0)
2.0ms
(- (exp x) 1.0)
2.0ms
(- (exp x) 1.0)
5.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify93.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0156394
1399367
21035363
32831363
45002363

prune195.0ms

Filtered
49 candidates to 72 candidates (-46.9%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New72072
Fresh011
Picked011
Done022
Total72476

Merged error: 0b

Counts
76 → 4

regimes47.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.4b

bsearch22.0ms

Steps
ItersRangePoint
7
-6.026155611867161e-05
-2.9945710652836337e-06
-6.178127787804643e-06

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03827
13827

end0.0ms

analyze458.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%62.5%12.5%4
25%56.2%18.8%5
28.1%50%21.9%6
29.7%46.9%23.5%7
30.5%45.3%24.3%8
30.8%44.9%24.3%9
31.2%44.5%24.3%10
31.3%44.3%24.4%11
31.4%44.3%24.4%12
31.4%44%24.5%13
31.5%43.8%24.8%14

sample1.6s

Algorithm
intervals
Results
807.0ms2268×body1280valid
370.0ms1606×body640valid
131.0ms2862×body80valid
122.0ms819×body320valid
44.0ms445×body160valid
0.0ms2×body80invalid

Profiling

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