Details

Time bar (total: 9.2s)

sample83.0ms

Algorithm
intervals
Results
17.0ms329×body80nan
8.0ms154×body80valid
8.0ms28×body1280valid
6.0ms29×body640valid
5.0ms30×body320valid
4.0ms21×body640nan
2.0ms9×body1280nan
2.0ms12×body320nan
2.0ms15×body160valid
1.0ms7×body160nan

simplify94.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214
done500214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (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)
13.7b
(- (* (/ (+ 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)))

rewrite150.0ms

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:
55.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms
(* (sqrt 2.0) t)
34.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
47.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
439.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
46.0ms
(* (sqrt 2.0) t)
226.0ms
(- (* (/ (+ 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)))

simplify68.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04461290
122061177
250021172
done50021172

prune356.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.0b

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.7b
(/ (pow l 2) x)
9.0b
(/ (pow t 2) x)
29.0b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite23.0ms

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))))
8.0ms
(/ (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)))))

series383.0ms

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))))
20.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
272.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify42.0ms

Counts
139 → 139
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0377811
11351724
25001715
done5001715

prune482.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
3.2b
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
9.0b
(/ (pow t 2) x)
29.0b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite14.0ms

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)
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
9.0ms
(/ (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)))))

series574.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(cbrt x)
88.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow t 2) x)
284.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify35.0ms

Counts
101 → 101
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0305760
11089656
25001645
done5001645

prune408.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
3.2b
(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))))
9.0b
(/ (pow t 2) x)
29.0b
(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)))))

rewrite17.0ms

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)
0.0ms
(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))))
9.0ms
(/ (pow t 2) x)
5.0ms
(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:
181.0ms
(cbrt x)
89.0ms
(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))))
19.0ms
(/ (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)))))

simplify37.0ms

Counts
101 → 101
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0310943
11056834
25001820
done5001820

prune436.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

regimes440.0ms

Accuracy

73.5% (6.4b remaining)

Error of 10.3b against oracle of 3.9b and baseline of 27.9b

bsearch680.0ms

Steps
ItersRangePoint
6
1.4492506646584313e+85
1.822198397165114e+86
2.1749908664970245e+85
8
3.253872409851107e-130
5.196545289398966e-127
3.2912161221926835e-130
11
2.854009960629658e-293
6.144753180559701e-264
9.909309527651243e-270
8
-3.536926816114651e-240
-2.6493665622057615e-244
-3.0886340565384557e-240
9
-1.5401742513156077e-163
-1.1631287859066171e-170
-6.6963672441100204e-164
6
-2.8371712079202784e+139
-6.825323247239397e+138
-9.583977798108111e+138

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083134
183134
done83134

end0.0ms

sample2.3s

Algorithm
intervals
Results
497.0ms10055×body80nan
274.0ms5079×body80valid
216.0ms830×body1280valid
206.0ms1027×body640valid
133.0ms556×body1280nan
118.0ms627×body640nan
100.0ms687×body320valid
57.0ms350×body320nan
38.0ms377×body160valid
19.0ms196×body160nan