Details

Time bar (total: 8.4s)

sample90.0ms

Algorithm
intervals
Results
31.0ms318×body80nan
10.0ms36×body1280valid
8.0ms166×body80valid
4.0ms23×body640valid
4.0ms17×body1280nan
3.0ms20×body320valid
3.0ms16×body640nan
2.0ms14×body320nan
1.0ms12×body160nan
1.0ms11×body160valid

simplify97.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b
(* (sqrt 2.0) t)
13.7b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.9b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
17.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms
(* (sqrt 2.0) t)
14.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
431.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
41.0ms
(* (sqrt 2.0) t)
223.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify64.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04461290
122061177
250021172

prune358.0ms

Filtered
102 candidates to 75 candidates (73.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.7b

localize17.0ms

Local error

Found 4 expressions with local error:

4.6b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.7b
(/ (pow l 2) x)
9.7b
(/ (pow t 2) x)
29.1b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 127
Calls
4 calls:
1.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
9.0ms
(/ (pow l 2) x)
5.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series377.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
270.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0377811
11351724
25001715

prune476.0ms

Filtered
139 candidates to 96 candidates (69.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
4.6b
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.7b
(/ (pow t 2) x)
29.1b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
12×unpow-prod-down
11×add-exp-log
8×add-cbrt-cube associate-/l*
7×pow1 sqrt-prod
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×div-exp associate-*r* associate-/r*
2×unswap-sqr
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod fma-udef div-inv
Counts
4 → 100
Calls
4 calls:
5.0ms
(* (sqrt 2.0) t)
1.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
5.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series399.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sqrt 2.0) t)
69.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
267.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify40.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0322666
11250592
25001586

prune376.0ms

Filtered
112 candidates to 78 candidates (69.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
4.6b
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.7b
(/ (pow t 2) x)
29.1b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
14×add-exp-log
12×unpow-prod-down sqrt-prod
11×add-cbrt-cube
10×pow1
9×associate-*l*
8×associate-/l*
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×div-exp pow-prod-down prod-exp associate-/r* cbrt-unprod
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r* pow-exp clear-num *-commutative fma-udef div-inv
Counts
4 → 102
Calls
4 calls:
9.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
1.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
5.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series404.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
64.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
24.0ms
(/ (pow t 2) x)
268.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify42.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0359733
11286640
25001630

prune384.0ms

Filtered
114 candidates to 79 candidates (69.3%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

regimes420.0ms

Accuracy

76.7% (5.6b remaining)

Error of 9.5b against oracle of 3.9b and baseline of 27.8b

bsearch692.0ms

Steps
ItersRangePoint
7
5.370742752958284e+102
9.052977485532749e+104
5.426154015794088e+103
9
1.3029797544721211e-186
2.584931216526496e-179
7.462272746999086e-184
7
1.8228355444078093e-268
1.1711784318322953e-266
3.8487763571868812e-267
9
1.63313445447925e-306
1.1671312290744826e-298
1.6693954462848767e-306
6
-4.9536353380982224e-232
-3.430410021188815e-233
-3.4906994589006823e-233
9
-6.053829993602053e+133
-1.5220798265964686e+128
-4.3793915188056946e+130

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068124
171124
274124
374124

end0.0ms

sample2.0s

Algorithm
intervals
Results
488.0ms9975×body80nan
257.0ms5121×body80valid
221.0ms882×body1280valid
198.0ms998×body640valid
142.0ms597×body1280nan
114.0ms574×body640nan
99.0ms670×body320valid
52.0ms359×body320nan
31.0ms329×body160valid
17.0ms181×body160nan