Details

Time bar (total: 8.5s)

sample81.0ms

Algorithm
intervals
Results
16.0ms308×body80nan
13.0ms18×body1280nan
9.0ms174×body80valid
6.0ms30×body640valid
6.0ms22×body1280valid
4.0ms18×body640nan
3.0ms21×body320valid
1.0ms10×body320nan
1.0ms9×body160valid
1.0ms7×body160nan

simplify95.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214

prune5.0ms

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))))
0.5b
(* (sqrt 2.0) t)
10.5b
(- (* (/ (+ 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)))

rewrite59.0ms

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)
19.0ms
(- (* (/ (+ 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)))

series1.8s

Counts
4 → 12
Calls
4 calls:
423.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
42.0ms
(* (sqrt 2.0) t)
212.0ms
(- (* (/ (+ 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)))

simplify62.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04461291
122061177
250021172

prune348.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.4b

localize17.0ms

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))))
5.5b
(/ (pow l 2) x)
10.0b
(/ (pow t 2) x)
28.7b
(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)))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(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)
24.0ms
(/ (pow t 2) x)
269.0ms
(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

prune482.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(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))))
10.0b
(/ (pow t 2) x)
28.7b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite11.0ms

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)))))

series571.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(cbrt x)
87.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
280.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify37.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0305747
11035659
25001648

prune411.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
3.8b
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) (* 4.0 (/ (pow t 2) x))))
10.0b
(/ (pow t 2) x)
28.7b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) (* 4.0 (/ (pow t 2) x)))))

rewrite11.0ms

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

series576.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(cbrt x)
88.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
287.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) (* 4.0 (/ (pow t 2) x)))))

simplify39.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0310943
11056834
25001820

prune426.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.5b

regimes332.0ms

Accuracy

73.9% (6.1b remaining)

Error of 9.7b against oracle of 3.6b and baseline of 27.1b

bsearch455.0ms

Steps
ItersRangePoint
9
6.5674376860864575e+41
3.160563175756606e+48
2.439864779519815e+48
5
2.5314598921169833e-163
7.493051701410122e-163
6.30041024948343e-163
9
-6.02957645582761e-302
-2.832827517419726e-308
-2.8785002221205043e-308
9
-3.8796894483799902e+115
-4.972566247523887e+110
-2.4044001424157714e+115

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06097
16397
26697
36697

end0.0ms

sample2.1s

Algorithm
intervals
Results
514.0ms10071×body80nan
266.0ms5079×body80valid
229.0ms878×body1280valid
201.0ms1007×body640valid
145.0ms587×body1280nan
115.0ms600×body640nan
98.0ms666×body320valid
56.0ms355×body320nan
37.0ms370×body160valid
18.0ms187×body160nan