Details

Time bar (total: 9.0s)

sample111.0ms

Algorithm
intervals
Results
26.0ms160×body80valid
21.0ms276×body80nan
11.0ms37×body640valid
8.0ms23×body1280nan
7.0ms18×body1280valid
6.0ms28×body320valid
3.0ms12×body640nan
2.0ms13×body160valid
1.0ms7×body320nan
1.0ms7×body160nan

simplify96.0ms

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: 44.9b

Counts
2 → 1

localize20.0ms

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)
14.5b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite65.0ms

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:
18.0ms
(/ (* (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)
21.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
17.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.0s

Counts
4 → 12
Calls
4 calls:
451.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
47.0ms
(* (sqrt 2.0) t)
227.0ms
(- (* (/ (+ 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)))

simplify64.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04461291
122061177
250021172

prune362.0ms

Filtered
102 candidates to 75 candidates (73.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New966102
Fresh000
Picked101
Done000
Total976103

Merged error: 6.3b

Counts
103 → 6

localize20.0ms

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))))
5.2b
(/ (pow l 2) x)
8.8b
(/ (pow t 2) x)
28.4b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite22.0ms

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))))
6.0ms
(/ (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)))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(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)
20.0ms
(/ (pow t 2) x)
284.0ms
(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
0377837
11450724
25001715

prune485.0ms

Filtered
139 candidates to 96 candidates (69.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1318139
Fresh145
Picked101
Done000
Total13312145

Merged error: 4.1b

Counts
145 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
3.8b
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
8.8b
(/ (pow t 2) x)
28.4b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite16.0ms

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

series417.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sqrt 2.0) t)
67.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
25.0ms
(/ (pow t 2) x)
279.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0321653
11261592
25001586

prune364.0ms

Filtered
112 candidates to 76 candidates (67.9%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1111112
Fresh11011
Picked011
Done000
Total11212124

Merged error: 4.1b

Counts
124 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
3.8b
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
8.8b
(/ (pow t 2) x)
28.4b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite12.0ms

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)
1.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
5.0ms
(/ (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)))))

series613.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(cbrt x)
102.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
20.0ms
(/ (pow t 2) x)
305.0ms
(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 (28.0ms)

IterNodesCost
0305747
11035659
25001648

prune361.0ms

Filtered
101 candidates to 73 candidates (72.3%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1010101
Fresh01010
Picked011
Done011
Total10112113

Merged error: 4.1b

Counts
113 → 12

regimes430.0ms

Accuracy

76.4% (5.5b remaining)

Error of 9.2b against oracle of 3.7b and baseline of 27.0b

bsearch229.0ms

Steps
ItersRangePoint
8
2.755145085308258e+110
7.118807562754038e+112
4.466400235178163e+111
9
-9.112786846721816e+33
-1.2853898846943825e+28
-9.014127391409104e+33

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05344
17244
27344
37344

end0.0ms

sample2.8s

Algorithm
intervals
Results
691.0ms9740×body80nan
373.0ms5063×body80valid
304.0ms833×body1280valid
297.0ms1067×body640valid
204.0ms566×body1280nan
169.0ms584×body640nan
142.0ms674×body320valid
76.0ms368×body320nan
54.0ms363×body160valid
27.0ms197×body160nan