Details

Time bar (total: 9.3s)

sample96.0ms

Algorithm
intervals
Results
30.0ms353×body80nan
8.0ms157×body80valid
8.0ms31×body1280nan
7.0ms28×body1280valid
7.0ms34×body640valid
5.0ms25×body640nan
4.0ms25×body320valid
1.0ms10×body320nan
1.0ms12×body160valid
1.0ms6×body160nan

simplify98.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (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)
13.4b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.4b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite76.0ms

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)
20.0ms
(- (* (/ (+ 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:
404.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
37.0ms
(* (sqrt 2.0) t)
207.0ms
(- (* (/ (+ 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

prune344.0ms

Filtered
102 candidates to 75 candidates (73.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize17.0ms

Local error

Found 4 expressions with local error:

3.4b
(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)
9.7b
(/ (pow t 2) x)
28.8b
(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:
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.0ms
(/ (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)))))

series354.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(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)
254.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0377811
11351724
25001715

prune470.0ms

Filtered
139 candidates to 96 candidates (69.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
3.4b
(fma 2.0 (pow t 2) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x))))
9.7b
(/ (pow t 2) x)
28.8b
(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)))))

rewrite42.0ms

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:
29.0ms
(* (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))))
4.0ms
(/ (pow t 2) x)
1.0ms
(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:
44.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
86.0ms
(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)
274.0ms
(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)))))

simplify80.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
07041652
133791419
250011377

prune687.0ms

Filtered
184 candidates to 122 candidates (66.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize27.0ms

Local error

Found 4 expressions with local error:

16.3b
(cbrt (pow (cbrt l) 4))
16.3b
(cbrt (pow (cbrt l) 4))
16.3b
(cbrt (pow (cbrt l) 4))
28.8b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (* (cbrt (pow (cbrt l) 4)) (cbrt (pow (cbrt l) 4))) (* (cbrt (pow (cbrt l) 4)) (/ (pow (cbrt l) 2) x))) (* 4.0 (/ (pow t 2) x)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
18×unpow-prod-down
15×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 75
Calls
4 calls:
2.0ms
(cbrt (pow (cbrt l) 4))
2.0ms
(cbrt (pow (cbrt l) 4))
2.0ms
(cbrt (pow (cbrt l) 4))
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (* (cbrt (pow (cbrt l) 4)) (cbrt (pow (cbrt l) 4))) (* (cbrt (pow (cbrt l) 4)) (/ (pow (cbrt l) 2) x))) (* 4.0 (/ (pow t 2) x)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
271.0ms
(cbrt (pow (cbrt l) 4))
271.0ms
(cbrt (pow (cbrt l) 4))
271.0ms
(cbrt (pow (cbrt l) 4))
276.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (* (cbrt (pow (cbrt l) 4)) (cbrt (pow (cbrt l) 4))) (* (cbrt (pow (cbrt l) 4)) (/ (pow (cbrt l) 2) x))) (* 4.0 (/ (pow t 2) x)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0196800
1468755
21557746
35001729

prune420.0ms

Filtered
87 candidates to 69 candidates (79.3%)
Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.6b

regimes484.0ms

Accuracy

75.6% (5.9b remaining)

Error of 9.8b against oracle of 3.9b and baseline of 28.0b

bsearch448.0ms

Steps
ItersRangePoint
8
1.245043086949984e+133
8.355688030489222e+136
1.3295537074089366e+133
8
3.9920941018400604e-199
1.0341623309317825e-196
8.363027552225931e-198
9
4.057362571362824e-285
4.0450842402039645e-278
5.316863584577416e-279
8
-2.3663462124314626e+100
-5.129643794534772e+97
-8.085419595728973e+99

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
065113
168113
271113
371113

end0.0ms

sample2.1s

Algorithm
intervals
Results
514.0ms10273×body80nan
267.0ms5121×body80valid
218.0ms859×body1280valid
198.0ms996×body640valid
153.0ms622×body1280nan
110.0ms583×body640nan
95.0ms639×body320valid
45.0ms320×body320nan
41.0ms385×body160valid
19.0ms198×body160nan