Details

Time bar (total: 22.8s)

sample297.0ms

Algorithm
intervals
Results
86.0ms359×body80nan
23.0ms172×body80valid
18.0ms30×body1280valid
13.0ms31×body640nan
13.0ms25×body640valid
7.0ms13×body1280nan
5.0ms17×body320nan
5.0ms17×body320valid
3.0ms12×body160valid
2.0ms8×body160nan

simplify4.7s

Counts
1 → 1
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
01827
14126
210026
323426
453126
5105126
6192926
7459326
done500026

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (* t t))
0.4b
(* (sqrt 2.0) t)
11.9b
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
22.3b
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×pow1
11×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*l*
7×sqrt-prod
6×add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×unswap-sqr
2×flip3-- sqrt-div *-commutative flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 78
Calls
4 calls:
22.0ms
(* 2.0 (* t t))
11.0ms
(* (sqrt 2.0) t)
40.0ms
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
41.0ms
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series814.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* 2.0 (* t t))
60.0ms
(* (sqrt 2.0) t)
272.0ms
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
454.0ms
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify1.3s

Counts
90 → 90
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01431437
13671359
217961247
done50001240

prune671.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 29.2b

localize30.0ms

Local error

Found 4 expressions with local error:

4.0b
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
5.3b
(/ (pow l 2) x)
8.3b
(/ (pow t 2) x)
27.4b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

rewrite24.0ms

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 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
9.0ms
(/ (pow l 2) x)
9.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

series406.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
28.0ms
(/ (pow l 2) x)
34.0ms
(/ (pow t 2) x)
240.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

simplify895.0ms

Counts
139 → 139
Iterations

Useful iterations: done (884.0ms)

IterNodesCost
02161767
13981621
215761429
done50001426

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b
(fma t t (* l (/ l x)))
4.0b
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x)))))
8.3b
(/ (pow t 2) x)
27.4b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x))))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×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×div-exp associate-/r* sqrt-prod
2×fma-udef
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
1.0ms
(fma t t (* l (/ l x)))
1.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x)))))
19.0ms
(/ (pow t 2) x)
4.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x))))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(fma t t (* l (/ l x)))
104.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x)))))
25.0ms
(/ (pow t 2) x)
261.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* l (/ l x))))))

simplify797.0ms

Counts
98 → 98
Iterations

Useful iterations: done (793.0ms)

IterNodesCost
01581364
12921263
211691121
done50011119

prune712.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(fma t t (/ (pow l (/ 2 2)) (/ x l)))
4.0b
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
8.3b
(/ (pow t 2) x)
27.4b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×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×div-exp associate-/r* sqrt-prod
2×fma-udef
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
0.0ms
(fma t t (/ (pow l (/ 2 2)) (/ x l)))
0.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
9.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

series540.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(fma t t (/ (pow l (/ 2 2)) (/ x l)))
141.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
35.0ms
(/ (pow t 2) x)
289.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

simplify627.0ms

Counts
98 → 98
Iterations

Useful iterations: done (624.0ms)

IterNodesCost
01591532
12981346
211571124
done50011119

prune628.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.4b

regimes1.1s

Accuracy

73% (6.4b remaining)

Error of 10.3b against oracle of 3.9b and baseline of 27.6b

bsearch840.0ms

Steps
ItersRangePoint
9
6.027114233911676e+43
4.1565058545339404e+49
1.70506510457761e+47
6
2.1503862826174094e-161
2.3313945744883712e-160
2.7697629478154104e-161
9
1.1526147498288588e-235
1.4384887770647992e-230
1.0155485322712369e-231
10
-1.7570278330957123e-32
-3.9436752905842844e-42
-2.603334902900383e-37

simplify23.0ms

Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
054151
165122
269120
371120
done71120

end0.0ms

sample6.5s

Algorithm
intervals
Results
1.3s5049×body80valid
1.2s10170×body80nan
866.0ms596×body1280nan
647.0ms1006×body640valid
548.0ms880×body1280valid
299.0ms642×body640nan
235.0ms656×body320valid
209.0ms364×body320nan
129.0ms409×body160valid
33.0ms160×body160nan