Details

Time bar (total: 10.9s)

sample106.0ms

Algorithm
intervals
Results
21.0ms336×body80nan
17.0ms160×body80valid
10.0ms33×body1280nan
9.0ms35×body640valid
7.0ms22×body1280valid
5.0ms21×body640nan
5.0ms25×body320valid
2.0ms14×body160valid
2.0ms9×body320nan
1.0ms10×body160nan

simplify102.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

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)
12.6b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
17.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite162.0ms

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:
60.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms
(* (sqrt 2.0) t)
33.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
55.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.7s

Counts
4 → 12
Calls
4 calls:
395.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
43.0ms
(* (sqrt 2.0) t)
197.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.1s
(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
04461290
122061177
250021172

prune692.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.3b

localize17.0ms

Local error

Found 4 expressions with local error:

3.0b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.5b
(/ (pow l 2) x)
6.8b
(/ (pow t 2) x)
24.5b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite28.0ms

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))))
9.0ms
(/ (pow l 2) x)
9.0ms
(/ (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)))))

series347.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
22.0ms
(/ (pow l 2) x)
17.0ms
(/ (pow t 2) x)
247.0ms
(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 (33.0ms)

IterNodesCost
0377811
11351725
25001715

prune725.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
3.0b
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
6.8b
(/ (pow t 2) x)
24.5b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt times-frac
23×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
9×add-exp-log
8×associate-/l*
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×cbrt-prod div-exp associate-/r* sqrt-prod
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow1/3 pow-exp clear-num fma-udef div-inv
Counts
4 → 89
Calls
4 calls:
1.0ms
(cbrt x)
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
9.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

series538.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt x)
80.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
17.0ms
(/ (pow t 2) x)
264.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify38.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0305747
11035659
25001648

prune739.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
3.0b
(fma 2.0 (pow t 2) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x))))
6.8b
(/ (pow t 2) x)
24.5b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt
77×times-frac
56×unpow-prod-down
46×add-cube-cbrt *-un-lft-identity
37×associate-*r*
35×add-exp-log
24×unswap-sqr
22×cbrt-prod
18×sqr-pow
12×div-exp prod-exp
11×add-cbrt-cube unpow2
10×associate-*l*
8×pow-to-exp pow-exp associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* sqrt-prod
2×cbrt-undiv cbrt-unprod div-inv
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num *-commutative fma-udef
Counts
4 → 172
Calls
4 calls:
43.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x))))
9.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x)))))

series422.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
87.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x))))
17.0ms
(/ (pow t 2) x)
272.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x)))))

simplify83.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07041604
129641400
250011363

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.3b

regimes605.0ms

Accuracy

77.1% (5.5b remaining)

Error of 9.4b against oracle of 4.0b and baseline of 27.9b

bsearch576.0ms

Steps
ItersRangePoint
4
2.6200720998945785e+73
4.738753520196159e+73
2.921906157655208e+73
10
1.1200479248291668e-155
8.021928499612576e-146
1.134979313002666e-155
8
1.2050335798233843e-229
1.47940694473299e-226
2.7018349819747363e-228
8
-1.6637674008041316e+41
-5.9303587624045785e+38
-1.5387064518011545e+41

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06587
18787
29187
39187

end0.0ms

sample2.6s

Algorithm
intervals
Results
653.0ms10046×body80nan
344.0ms5111×body80valid
296.0ms896×body1280valid
258.0ms998×body640valid
181.0ms580×body1280nan
159.0ms636×body640nan
116.0ms617×body320valid
69.0ms353×body320nan
50.0ms378×body160valid
24.0ms196×body160nan