Details

Time bar (total: 8.0s)

sample85.0ms

Algorithm
intervals
Results
26.0ms316×body80nan
8.0ms43×body640valid
8.0ms156×body80valid
7.0ms29×body1280valid
4.0ms16×body1280nan
4.0ms23×body320valid
3.0ms17×body640nan
2.0ms12×body320nan
1.0ms5×body160nan
0.0ms5×body160valid

simplify97.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.4b

localize18.0ms

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))))
0.4b
(* (sqrt 2.0) t)
11.9b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.4b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite77.0ms

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:
31.0ms
(/ (* (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))
24.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
446.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
46.0ms
(* (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)))

simplify63.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04461291
122061177
250021172

prune352.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.0b

localize18.0ms

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))))
5.2b
(/ (pow l 2) x)
9.0b
(/ (pow t 2) x)
28.2b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite14.0ms

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))))
4.0ms
(/ (pow l 2) x)
4.0ms
(/ (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)))))

series391.0ms

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))))
20.0ms
(/ (pow l 2) x)
26.0ms
(/ (pow t 2) x)
279.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0377811
11351724
25001715

prune484.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
4.0b
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
9.0b
(/ (pow t 2) x)
28.2b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs 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:
5.0ms
(* (sqrt 2.0) t)
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs 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 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sqrt 2.0) t)
59.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow t 2) x)
157.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify48.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0356727
11467654
25001649

prune404.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(* t (sqrt 2.0))
4.0b
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
9.0b
(/ (pow t 2) x)
28.2b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs 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-*r*
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×div-exp associate-*l* 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
(* t (sqrt 2.0))
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs 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 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series277.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* t (sqrt 2.0))
64.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow t 2) x)
154.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0361741
11499653
25002648

prune376.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.7b

regimes273.0ms

Accuracy

72.6% (6.5b remaining)

Error of 10.3b against oracle of 3.8b and baseline of 27.4b

bsearch638.0ms

Steps
ItersRangePoint
6
1.772474996099602e+22
9.816334120698393e+22
9.67333495452905e+22
7
1.511609718335987e-222
1.5314766828107433e-220
8.296676812285223e-221
8
9.830296204345552e-280
4.771728286328876e-277
4.692908969753362e-277
8
-5.5469828895486275e-251
-5.367476004269873e-254
-4.917024371515258e-252
5
-5.1248532454389843e-166
-1.4680611298719264e-166
-5.0482585651684744e-166
10
-5.429880568053305e+57
-4.398563231493774e+43
-2.3830943467781888e+52

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067140
167140

end0.0ms

sample2.0s

Algorithm
intervals
Results
494.0ms10166×body80nan
259.0ms5061×body80valid
216.0ms866×body1280valid
203.0ms1048×body640valid
147.0ms622×body1280nan
110.0ms591×body640nan
96.0ms662×body320valid
44.0ms322×body320nan
35.0ms363×body160valid
17.0ms181×body160nan