Details

Time bar (total: 9.2s)

sample85.0ms

Algorithm
intervals
Results
16.0ms310×body80nan
9.0ms167×body80valid
7.0ms32×body640valid
7.0ms25×body1280valid
5.0ms19×body1280nan
3.0ms15×body640nan
3.0ms17×body320valid
2.0ms15×body160valid
2.0ms10×body320nan
0.0ms5×body160nan

simplify96.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

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))))
0.4b
(* (sqrt 2.0) t)
12.1b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.7b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite56.0ms

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)
14.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
16.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.0s

Counts
4 → 12
Calls
4 calls:
448.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
49.0ms
(* (sqrt 2.0) t)
225.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.3s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify68.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04461291
122061177
250021172

prune369.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.2b

localize17.0ms

Local error

Found 4 expressions with local error:

4.8b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.1b
(/ (pow l 2) x)
9.5b
(/ (pow t 2) x)
27.6b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite17.0ms

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)))))

series388.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
24.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
279.0ms
(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 (32.0ms)

IterNodesCost
0377837
11450724
25001715

prune500.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
4.8b
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.5b
(/ (pow t 2) x)
27.6b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite15.0ms

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

series418.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sqrt 2.0) t)
72.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow t 2) x)
279.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0322653
11220592
25001586

prune409.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 4)
1.8b
(* (pow (cbrt t) 4) (/ (pow (cbrt t) 2) x))
4.8b
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (* (pow (cbrt t) 4) (/ (pow (cbrt t) 2) x)))))
27.6b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (* (pow (cbrt t) 4) (/ (pow (cbrt t) 2) x))))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt
53×times-frac
50×unpow-prod-down
37×associate-*r*
32×add-cube-cbrt *-un-lft-identity
31×add-exp-log
25×cbrt-prod
24×unswap-sqr
15×sqr-pow
12×prod-exp
10×associate-*l*
9×div-exp add-cbrt-cube
8×pow-to-exp pow-exp
7×unpow2
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow sqrt-prod
2×pow-pow cbrt-unprod
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 associate-*r/ *-commutative fma-udef div-inv
Counts
4 → 144
Calls
4 calls:
3.0ms
(pow (cbrt t) 4)
22.0ms
(* (pow (cbrt t) 4) (/ (pow (cbrt t) 2) x))
1.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (* (pow (cbrt t) 4) (/ (pow (cbrt t) 2) x)))))
2.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (* (pow (cbrt t) 4) (/ (pow (cbrt t) 2) x))))))

series705.0ms

Counts
4 → 12
Calls
4 calls:
238.0ms
(pow (cbrt t) 4)
50.0ms
(* (pow (cbrt t) 4) (/ (pow (cbrt t) 2) x))
102.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (* (pow (cbrt t) 4) (/ (pow (cbrt t) 2) x)))))
314.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (* (pow (cbrt t) 4) (/ (pow (cbrt t) 2) x))))))

simplify74.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06431453
127281271
250011233

prune609.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.1b

regimes540.0ms

Accuracy

73.6% (6.2b remaining)

Error of 10.0b against oracle of 3.8b and baseline of 27.3b

bsearch432.0ms

Steps
ItersRangePoint
7
2.896305437726327e+111
1.3118630056926933e+113
1.2953282500941115e+113
4
-2.0786106758946992e-238
-1.3297541091157469e-238
-1.4640217334256062e-238
9
-1.6835204431162708e-199
-2.9969892637229514e-206
-2.958463792680025e-203
9
-1.7953405712417382e-26
-1.5166399548635069e-33
-1.7657799131066967e-26

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07195
17195

end0.0ms

sample2.2s

Algorithm
intervals
Results
541.0ms10275×body80nan
280.0ms5099×body80valid
240.0ms878×body1280valid
216.0ms1040×body640valid
155.0ms596×body1280nan
128.0ms616×body640nan
91.0ms593×body320valid
55.0ms367×body320nan
40.0ms390×body160valid
18.0ms181×body160nan