Details

Time bar (total: 11.3s)

sample3.2s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0.457764%

Guaranteed chance to sample good point: 29.278313%

Results
36.0ms80×body1280valid
15.0ms60×body640valid
4.0ms26×body320valid
4.0ms85×body80overflowed
3.0ms71×body80valid
2.0ms19×body160valid

simplify430.0ms

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: 45.3b

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))
5.2b
(- (exp x) 1.0)
5.6b
(- (exp (* 2.0 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:
9.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms
(- (exp x) 1.0)
6.0ms
(- (exp (* 2.0 x)) 1.0)

series32.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(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)

simplify127.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 3 (105.0ms)

IterNodesCost
03871380
110541314
242651301
350021293

prune249.0ms

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

localize12.0ms

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)))
0.4b
(/ (pow x 2) (sqrt 2.0))
0.4b
(/ x (sqrt 2.0))

rewrite50.0ms

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)))))
23.0ms
(* (/ (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))

series26.0ms

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)))))
7.0ms
(* (/ (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))

simplify89.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
07231889
130421708
250011694

prune499.0ms

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

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2312233
Fresh022
Picked101
Done000
Total2324236

Merged error: 0.0b

Counts
236 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt 2.0))
9.2b
(cbrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
9.2b
(cbrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
9.2b
(cbrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
12×cbrt-div sqrt-prod
9×cbrt-prod
6×add-exp-log flip3-+ associate-*r/ frac-add associate-/r* add-cbrt-cube flip-+
4×pow1 add-log-exp
3×pow1/3 associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 84
Calls
4 calls:
4.0ms
(/ x (sqrt 2.0))
8.0ms
(cbrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
8.0ms
(cbrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
8.0ms
(cbrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))

series54.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ x (sqrt 2.0))
15.0ms
(cbrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
15.0ms
(cbrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
16.0ms
(cbrt (+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04771972
118271858
250011830

prune807.0ms

Filtered
77 candidates to 96 candidates (-24.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New96096
Fresh033
Picked011
Done000
Total964100

Merged error: 0.0b

Counts
100 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (pow x 2) (sqrt 2.0))
0.4b
(/ x (sqrt 2.0))
5.7b
(log (exp (/ x (sqrt 2.0))))
9.6b
(+ (* 0.5 (log (exp (/ x (sqrt 2.0))))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
67×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×sqrt-prod
23×log-pow
22×exp-prod
21×unpow-prod-down
12×associate-/r*
11×add-exp-log associate-/l*
9×log-prod add-log-exp
8×add-cbrt-cube
7×unpow2 sqr-pow
6×associate-+l+
5×pow1
4×div-exp
3×distribute-rgt-in distribute-lft-in sum-log div-inv
2×cbrt-undiv frac-2neg clear-num
1×+-commutative pow-to-exp associate-+r+ flip3-+ rem-log-exp pow-exp flip-+
Counts
4 → 168
Calls
4 calls:
6.0ms
(/ (pow x 2) (sqrt 2.0))
4.0ms
(/ x (sqrt 2.0))
6.0ms
(log (exp (/ x (sqrt 2.0))))
12.0ms
(+ (* 0.5 (log (exp (/ x (sqrt 2.0))))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

series23.0ms

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

simplify54.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04621300
116041139
250021121

prune375.0ms

Filtered
110 candidates to 180 candidates (-63.6%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1800180
Fresh022
Picked011
Done011
Total1804184

Merged error: 0.0b

Counts
184 → 4

regimes48.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.1b

bsearch27.0ms

Steps
ItersRangePoint
10
-7060.6252316046075
-1.3782998726997336e-09
-1.0310902685697735e-07

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04029
14029

end0.0ms

sample4.9s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0.457764%

Guaranteed chance to sample good point: 29.278313%

Results
839.0ms2247×body1280valid
415.0ms1695×body640valid
138.0ms865×body320valid
136.0ms2796×body80valid
118.0ms2667×body80overflowed
42.0ms397×body160valid
0.0ms1×body80invalid

Profiling

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