Details

Time bar (total: 7.9s)

sample94.0ms

Algorithm
intervals
Results
23.0ms157×body80valid
16.0ms330×body80nan
8.0ms35×body640valid
7.0ms28×body1280valid
5.0ms25×body640nan
4.0ms17×body1280nan
3.0ms23×body320valid
2.0ms16×body320nan
1.0ms13×body160valid
0.0ms5×body160nan

simplify94.0ms

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: 40.5b

localize24.0ms

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)
12.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
16.7b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite68.0ms

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:
24.0ms
(/ (* (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:
431.0ms
(/ (* (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)
220.0ms
(- (* (/ (+ 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)))

simplify70.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04461290
122061177
250021172

prune357.0ms

Filtered
102 candidates to 75 candidates (73.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.4b

localize18.0ms

Local error

Found 4 expressions with local error:

3.8b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.0b
(/ (pow l 2) x)
8.7b
(/ (pow t 2) x)
23.1b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite13.0ms

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)))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
275.0ms
(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

prune481.0ms

Filtered
139 candidates to 96 candidates (69.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 2.0) t)
3.8b
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
8.7b
(/ (pow t 2) x)
23.1b
(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)))))

series405.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sqrt 2.0) t)
70.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow t 2) x)
272.0ms
(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
112 → 112
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0321653
11261592
25001586

prune384.0ms

Filtered
112 candidates to 77 candidates (68.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
3.8b
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
8.7b
(/ (pow t 2) x)
23.1b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
21×add-exp-log
17×pow1
12×unpow-prod-down add-cbrt-cube
8×pow-prod-down prod-exp cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×div-exp associate-/r* sqrt-prod
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r* associate-*l* pow-exp clear-num *-commutative fma-udef div-inv
Counts
4 → 100
Calls
4 calls:
21.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (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)))))

series420.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
65.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
24.0ms
(/ (pow t 2) x)
278.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0371843
11422691
25002641

prune376.0ms

Filtered
112 candidates to 75 candidates (67.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

regimes391.0ms

Accuracy

73.7% (6.2b remaining)

Error of 10.3b against oracle of 4.1b and baseline of 27.7b

bsearch110.0ms

Steps
ItersRangePoint
6
9.245184352268912e-36
5.152775890346169e-35
5.05745477322558e-35
2
-1.3714823081983576e+148
-1.205437152500063e+148
-1.2503014417639997e+148

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05349
15349

end0.0ms

sample2.1s

Algorithm
intervals
Results
511.0ms10218×body80nan
265.0ms5061×body80valid
224.0ms886×body1280valid
204.0ms1028×body640valid
151.0ms610×body1280nan
117.0ms620×body640nan
102.0ms661×body320valid
49.0ms338×body320nan
36.0ms364×body160valid
18.0ms177×body160nan