Details

Time bar (total: 8.1s)

sample93.0ms

Algorithm
intervals
Results
30.0ms329×body80nan
10.0ms36×body1280valid
8.0ms152×body80valid
6.0ms28×body640valid
4.0ms29×body320valid
4.0ms16×body1280nan
3.0ms16×body640nan
2.0ms15×body320nan
1.0ms11×body160valid
1.0ms6×body160nan

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: 46.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b
(* (sqrt 2.0) t)
14.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.1b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite75.0ms

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:
29.0ms
(/ (* (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)
13.0ms
(- (* (/ (+ 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)))

series1.8s

Counts
4 → 12
Calls
4 calls:
418.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
39.0ms
(* (sqrt 2.0) t)
212.0ms
(- (* (/ (+ 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 (50.0ms)

IterNodesCost
04461290
122061177
250021172

prune356.0ms

Filtered
102 candidates to 75 candidates (73.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.8b

localize19.0ms

Local error

Found 4 expressions with local error:

4.0b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
7.4b
(/ (pow l 2) x)
9.7b
(/ (pow t 2) x)
28.9b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite17.0ms

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:
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
7.0ms
(/ (pow l 2) x)
5.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series364.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(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)
18.0ms
(/ (pow t 2) x)
261.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0377837
11450724
25001715

prune485.0ms

Filtered
139 candidates to 96 candidates (69.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 2.0) t)
4.0b
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
9.7b
(/ (pow t 2) x)
28.9b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite13.0ms

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:
4.0ms
(* (sqrt 2.0) t)
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

series382.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (sqrt 2.0) t)
67.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
256.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0321666
11291592
25001586

prune369.0ms

Filtered
112 candidates to 77 candidates (68.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
4.0b
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
9.7b
(/ (pow t 2) x)
28.9b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite27.0ms

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:
18.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
66.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
255.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0358733
11338640
25002630

prune378.0ms

Filtered
114 candidates to 79 candidates (69.3%)
Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.2b

regimes525.0ms

Accuracy

76.2% (5.6b remaining)

Error of 9.7b against oracle of 4.1b and baseline of 27.7b

bsearch393.0ms

Steps
ItersRangePoint
9
3.7850773704166493e+129
1.6704818658589414e+135
1.608798848532617e+131
6
4.706788075623402e-169
6.068595776665365e-168
9.713260788920249e-169
8
9.445409381569534e-197
4.675323760162538e-193
6.808028029233765e-195
6
-9.223758137202775e+53
-1.1417874782087954e+53
-5.468362385573983e+53

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06881
18781
28881
38881

end0.0ms

sample2.1s

Algorithm
intervals
Results
499.0ms9991×body80nan
267.0ms5035×body80valid
240.0ms921×body1280valid
200.0ms1008×body640valid
147.0ms608×body1280nan
123.0ms603×body640nan
94.0ms639×body320valid
48.0ms323×body320nan
39.0ms397×body160valid
18.0ms183×body160nan