Details

Time bar (total: 7.8s)

sample340.0ms

Algorithm
intervals
Results
45.0ms234×body10240exit
20.0ms363×body80nan
9.0ms230×body80valid
2.0ms30×body160valid

simplify70.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1287
2407
3737
41767
55597
626267
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: 5.5b

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)))
0.1b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
6.0b
(- (exp (* 2.0 x)) 1.0)
6.1b
(- (exp x) 1.0)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt
81×*-un-lft-identity
51×times-frac
31×sqrt-prod
29×add-cube-cbrt
26×distribute-lft-out-- difference-of-squares
15×sqrt-div
10×associate-/r* associate-/l*
8×add-log-exp
6×add-exp-log flip3-- add-cbrt-cube flip--
5×pow1
4×associate-/r/ associate-/l/
2×sub-neg rem-sqrt-square frac-2neg diff-log clear-num div-inv
1×cbrt-undiv sqrt-pow1 pow1/2 div-sub div-exp
Counts
4 → 137
Calls
4 calls:
15.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
13.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
7.0ms
(- (exp (* 2.0 x)) 1.0)
6.0ms
(- (exp x) 1.0)

series211.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
56.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
35.0ms
(- (exp (* 2.0 x)) 1.0)
23.0ms
(- (exp x) 1.0)

simplify122.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
04071530
110731476
243061460
350021452

prune371.0ms

Filtered
149 candidates to 102 candidates (68.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1454149
Fresh000
Picked101
Done000
Total1464150

Merged error: 0.0b

Counts
150 → 4

localize16.0ms

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))
6.1b
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
6.1b
(- (exp x) 1.0)

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
136×add-sqr-sqrt
121×sqrt-prod
100×*-un-lft-identity
62×sqrt-div
51×associate-*r*
49×difference-of-squares
47×times-frac
38×frac-times
32×distribute-lft-out--
29×associate-/l*
27×add-cube-cbrt
21×flip3-+ flip-+
19×associate-*r/
15×associate-/r*
10×add-log-exp
7×pow1
6×flip3-- flip-- associate-/l/
5×associate-*l*
4×add-exp-log clear-num add-cbrt-cube distribute-lft-out unswap-sqr
3×rem-sqrt-square frac-2neg un-div-inv
2×sub-neg sqrt-pow1 diff-log associate-*l/ associate-/r/
1×+-commutative pow1/2 pow-prod-down sum-log *-commutative div-inv
Counts
4 → 183
Calls
4 calls:
44.0ms
(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
9.0ms
(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms
(- (exp x) 1.0)

series441.0ms

Counts
4 → 12
Calls
4 calls:
333.0ms
(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
45.0ms
(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
48.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms
(- (exp x) 1.0)

simplify120.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
09264153
142874082
250014065

prune512.0ms

Filtered
195 candidates to 113 candidates (57.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1932195
Fresh213
Picked011
Done000
Total1954199

Merged error: 0.0b

Counts
199 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
0.1b
(* (sqrt (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))) (sqrt (* (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0)))))
6.1b
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
6.1b
(- (exp x) 1.0)

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
558×sqrt-div
266×add-sqr-sqrt
238×frac-times
223×sqrt-prod
163×*-un-lft-identity
124×flip3-+ flip-+
122×associate-*r*
119×associate-*r/
87×associate-/l*
79×difference-of-squares
53×times-frac
52×distribute-lft-out--
45×associate-/r*
44×add-cube-cbrt
34×unswap-sqr
19×associate-*l*
18×associate-/l/
12×flip3-- clear-num flip--
11×pow1
10×add-log-exp
9×frac-2neg un-div-inv
8×associate-*l/
6×add-exp-log add-cbrt-cube distribute-lft-out
5×pow-prod-down
4×sqrt-pow1
2×sub-neg pow1/2 diff-log associate-/r/ *-commutative
1×+-commutative sqrt-unprod prod-exp sum-log cbrt-unprod div-inv
Counts
4 → 348
Calls
4 calls:
9.0ms
(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
92.0ms
(* (sqrt (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))) (sqrt (* (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0)))))
12.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms
(- (exp x) 1.0)

series449.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
335.0ms
(* (sqrt (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))) (sqrt (* (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0)))))
48.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
22.0ms
(- (exp x) 1.0)

simplify114.0ms

Algorithm
egg-herbie
Counts
360 → 360
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
0139412500
1500112270

prune1.3s

Filtered
360 candidates to 213 candidates (59.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New3600360
Fresh022
Picked011
Done011
Total3604364

Merged error: 0.0b

Counts
364 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* 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)))
0.3b
(/ (pow x 2) (sqrt 2.0))
0.5b
(/ x (sqrt 2.0))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
123×times-frac
119×*-un-lft-identity
99×add-cube-cbrt
82×sqrt-prod
57×associate-*l*
50×unpow-prod-down
43×associate-/l*
42×associate-/r*
34×frac-times
28×frac-add
26×associate-*r/
21×add-exp-log
18×flip3-- flip-- unpow2 sqr-pow
17×associate-*l/
15×flip3-+ flip-+
13×add-cbrt-cube
10×associate-+r+ distribute-lft-out
9×clear-num add-log-exp unswap-sqr
7×frac-2neg div-exp
6×pow1 associate-*r*
4×distribute-rgt-in sub-neg distribute-lft-in prod-exp un-div-inv
3×cbrt-undiv sum-log div-inv
2×+-commutative pow-to-exp pow-exp cbrt-unprod difference-of-squares
1×pow-prod-down *-commutative distribute-lft-out--
Counts
4 → 306
Calls
4 calls:
64.0ms
(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
25.0ms
(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
7.0ms
(/ (pow x 2) (sqrt 2.0))
4.0ms
(/ x (sqrt 2.0))

series283.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
71.0ms
(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
64.0ms
(/ (pow x 2) (sqrt 2.0))
54.0ms
(/ x (sqrt 2.0))

simplify66.0ms

Algorithm
egg-herbie
Counts
318 → 318
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013843923
150013682

prune683.0ms

Filtered
318 candidates to 189 candidates (59.4%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New3162318
Fresh011
Picked101
Done022
Total3175322

Merged error: 0.0b

Counts
322 → 5

regimes39.0ms

Accuracy

80.5% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 4.2b

bsearch9.0ms

Steps
ItersRangePoint
1
-1.6476304282685804e-13
-1.5414983808378942e-13
-1.621097416410909e-13

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04656
14656

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s6405×body10240exit
392.0ms12785×body80nan
235.0ms7286×body80valid
70.0ms834×body160valid