Details

Time bar (total: 28.9s)

sample359.0ms

Algorithm
intervals
Results
46.0ms22×body640nan
45.0ms32×body1280valid
36.0ms12×body160valid
22.0ms322×body80nan
14.0ms156×body80valid
11.0ms38×body640valid
8.0ms23×body1280nan
4.0ms18×body320valid
2.0ms10×body320nan
1.0ms5×body160nan

simplify6.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01827
13927
29327
318927
439727
566127
6112227
7262427
8413127
done500027

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize35.0ms

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)
13.9b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite251.0ms

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×sqrt-div
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 diff-log pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
118.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
15.0ms
(* (sqrt 2.0) t)
48.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
64.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.6s

Counts
4 → 12
Calls
4 calls:
563.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
75.0ms
(* (sqrt 2.0) t)
294.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.4s

Counts
92 → 92
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01682472
14142283
215522077
done50002025

prune446.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.6b

localize24.0ms

Local error

Found 4 expressions with local error:

4.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
7.8b
(/ (pow l 2) x)
9.2b
(/ (pow t 2) x)
27.3b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite107.0ms

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×associate-*r/ add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r* add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×sqrt-prod
2×cbrt-undiv pow-to-exp associate-+r+ frac-2neg pow-exp clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 130
Calls
4 calls:
24.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
18.0ms
(/ (pow l 2) x)
21.0ms
(/ (pow t 2) x)
39.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
32.0ms
(/ (pow l 2) x)
34.0ms
(/ (pow t 2) x)
217.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify1.3s

Counts
142 → 142
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02542317
15352084
217251868
done50011862

prune691.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.0b

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
4.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
9.2b
(/ (pow t 2) x)
27.3b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
477×times-frac
208×add-sqr-sqrt
207×add-cube-cbrt *-un-lft-identity
176×unpow-prod-down
63×cbrt-prod unpow2 sqr-pow
49×add-exp-log
40×associate-/r*
31×div-exp
14×associate-/l*
13×pow-exp
11×add-cbrt-cube
9×pow-to-exp div-inv
8×associate-*r/
6×add-log-exp
5×pow1
4×cbrt-undiv flip3-+ sqrt-div frac-add prod-exp flip-+
3×sqrt-prod
2×associate-+r+ frac-2neg clear-num
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log associate-/r/
Counts
4 → 375
Calls
4 calls:
52.0ms
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
38.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
17.0ms
(/ (pow t 2) x)
21.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

series498.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
130.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
25.0ms
(/ (pow t 2) x)
270.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

simplify3.5s

Counts
387 → 387
Iterations

Useful iterations: 2 (1.9s)

IterNodesCost
069910732
114938400
249707038
done50007038

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.0b

localize49.0ms

Local error

Found 4 expressions with local error:

27.3b
(sqrt (* (* (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))))
28.2b
(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))
28.2b
(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))
28.2b
(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite311.0ms

Algorithm
rewrite-expression-head
Rules
336×associate-*r/
312×cbrt-div
176×frac-times
156×flip3-+ frac-add flip-+
124×sqrt-div
44×associate-*l/
24×pow1
15×sqrt-pow1
12×pow1/3
9×cbrt-prod pow-prod-up
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log add-cbrt-cube add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 193
Calls
4 calls:
229.0ms
(sqrt (* (* (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))))
12.0ms
(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))
13.0ms
(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))
25.0ms
(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
269.0ms
(sqrt (* (* (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))))
303.0ms
(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))
304.0ms
(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))
561.0ms
(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify1.3s

Counts
205 → 205
Iterations

Useful iterations: done (1.3s)

IterNodesCost
058026283
1100023917
2183121846
done500020627

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.0b

regimes555.0ms

Accuracy

71.2% (7.1b remaining)

Error of 11.0b against oracle of 3.9b and baseline of 28.4b

bsearch997.0ms

Steps
ItersRangePoint
9
3.5307849290302813e-79
1.4309834081351868e-71
1.4086343395051824e-71
8
1.9331730416670513e-145
3.203389628538628e-142
1.96678984226064e-145
7
2.9864185856163577e-279
3.6043515955327495e-277
3.155486028136924e-278
7
-4.881804416771232e-192
-8.553073611070034e-194
-1.8378980932293354e-192
10
-2.153678170399452e-149
-7.582263287327444e-161
-2.7094616069098305e-160
7
-3.61369871224165e+84
-8.523850575778694e+82
-3.489486864712887e+84

simplify20.0ms

Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
066265
181230
done81230

end0.0ms

sample3.4s

Algorithm
intervals
Results
728.0ms10246×body80nan
394.0ms5071×body80valid
326.0ms895×body1280valid
299.0ms1045×body640valid
210.0ms605×body1280nan
168.0ms603×body640nan
132.0ms603×body320valid
65.0ms320×body320nan
58.0ms386×body160valid
23.0ms175×body160nan