Details

Time bar (total: 11.1s)

sample144.0ms

Algorithm
intervals
Results
40.0ms309×body80nan
17.0ms154×body80valid
15.0ms39×body640valid
14.0ms30×body1280valid
12.0ms25×body1280nan
8.0ms22×body640nan
6.0ms22×body320valid
2.0ms12×body160nan
2.0ms8×body320nan
2.0ms11×body160valid

simplify94.0ms

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: 45.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
0.5b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
14.7b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.1b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite74.0ms

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:
5.0ms
(* (sqrt 2.0) t)
23.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
13.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
30.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (sqrt 2.0) t)
427.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
214.0ms
(- (* (/ (+ 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)))

simplify65.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04461290
122061177
250021172

prune365.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.9b

localize21.0ms

Local error

Found 4 expressions with local error:

3.7b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
8.3b
(/ (pow l 2) x)
9.3b
(/ (pow t 2) x)
28.5b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite14.0ms

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))))
4.0ms
(/ (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)))))

series384.0ms

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))))
19.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
275.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify46.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0377811
11351724
25001715

prune497.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (* (sqrt 2.0) t) (sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))))
3.7b
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.3b
(/ (pow t 2) x)
28.5b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
27×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
14×add-exp-log
12×unpow-prod-down
11×add-cbrt-cube
9×associate-/r* sqrt-prod associate-/l*
5×pow1 div-exp
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×cbrt-undiv
2×frac-2neg clear-num div-inv
1×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp prod-exp cbrt-unprod fma-udef
Counts
4 → 105
Calls
4 calls:
5.0ms
(/ (* (sqrt 2.0) t) (sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))))
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
8.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series502.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (* (sqrt 2.0) t) (sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))))
68.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 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 (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03741045
11575927
25001921

prune395.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize24.0ms

Local error

Found 4 expressions with local error:

9.3b
(/ (pow t 2) x)
28.5b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))
28.5b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))
28.5b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity times-frac
12×unpow-prod-down
9×add-exp-log sqrt-prod
8×associate-/l*
7×pow1
6×add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r*
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 96
Calls
4 calls:
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series814.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(/ (pow t 2) x)
266.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))
265.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))
265.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify163.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0237796
1781736
24596723
35001723

prune513.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

regimes328.0ms

Accuracy

75.5% (5.8b remaining)

Error of 9.7b against oracle of 3.9b and baseline of 27.4b

bsearch924.0ms

Steps
ItersRangePoint
10
2.93431907672103e+33
2.2751499328762104e+43
3.0890860106314964e+41
9
3.259559301848564e-230
2.9187828048320224e-222
4.0588751522494764e-230
10
1.8225108733483394e-283
3.128387530648835e-268
2.812190751433782e-269
7
-1.309735712265202e-248
-6.1447451134247286e-251
-7.158971193644144e-250
10
-5.21421466722245e-164
-2.34619512224237e-179
-2.398429761188533e-164
0
-7.918636126216888e+114
-7.662623262413979e+114
-7.790629694315434e+114

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077162
177162

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.0s9916×body80nan
550.0ms5022×body80valid
425.0ms889×body1280valid
410.0ms1086×body640valid
267.0ms574×body1280nan
231.0ms625×body640nan
191.0ms668×body320valid
98.0ms351×body320nan
66.0ms335×body160valid
34.0ms178×body160nan