Details

Time bar (total: 7.7s)

sample94.0ms

Algorithm
intervals
Results
15.0ms303×body80nan
8.0ms154×body80valid
7.0ms37×body640valid
7.0ms28×body1280valid
7.0ms26×body1280nan
4.0ms22×body640nan
3.0ms21×body320valid
2.0ms15×body320nan
2.0ms16×body160valid
1.0ms5×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 43.8b

Counts
2 → 1

localize27.0ms

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)
13.0b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.0b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite52.0ms

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)
13.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
15.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
439.0ms
(/ (* (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)
224.0ms
(- (* (/ (+ 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)))

simplify66.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04461291
122061177
250021172

prune334.0ms

Filtered
102 candidates to 75 candidates (73.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New984102
Fresh000
Picked101
Done000
Total994103

Merged error: 5.3b

Counts
103 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

5.6b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
7.1b
(/ (pow l 2) x)
7.8b
(/ (pow t 2) x)
26.4b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite16.0ms

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))))
5.0ms
(/ (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)))))

series387.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(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)
19.0ms
(/ (pow t 2) x)
277.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0377811
11351724
25001715

prune436.0ms

Filtered
139 candidates to 96 candidates (69.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1327139
Fresh033
Picked101
Done000
Total13310143

Merged error: 3.3b

Counts
143 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 2.0) t)
5.6b
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
7.8b
(/ (pow t 2) x)
26.4b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite14.0ms

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 (/ l x)) (* 4.0 (/ (pow t 2) x))))
5.0ms
(/ (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)))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sqrt 2.0) t)
63.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
23.0ms
(/ (pow t 2) x)
262.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0321666
11291592
25001586

prune332.0ms

Filtered
112 candidates to 77 candidates (68.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1102112
Fresh279
Picked101
Done000
Total1139122

Merged error: 3.3b

Counts
122 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
5.6b
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
7.8b
(/ (pow t 2) x)
26.4b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite24.0ms

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:
10.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
1.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l 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 (/ l x)) (* 4.0 (/ (pow t 2) x)))))

series409.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
80.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
265.0ms
(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 (39.0ms)

IterNodesCost
0371843
11422691
25002641

prune332.0ms

Filtered
112 candidates to 75 candidates (67.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1102112
Fresh088
Picked011
Done000
Total11011121

Merged error: 3.3b

Counts
121 → 11

regimes401.0ms

Accuracy

78% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 27.6b

bsearch170.0ms

Steps
ItersRangePoint
5
1.0369090885935443e+118
2.266299367795916e+118
2.024595502873266e+118
9
-2.4391232837537343e+50
-5.437652073963712e+44
-3.416831882302761e+49

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05461
15461

end0.0ms

sample2.0s

Algorithm
intervals
Results
496.0ms9941×body80nan
262.0ms5133×body80valid
205.0ms813×body1280valid
199.0ms1007×body640valid
144.0ms586×body1280nan
113.0ms592×body640nan
99.0ms669×body320valid
48.0ms336×body320nan
38.0ms378×body160valid
21.0ms204×body160nan