Details

Time bar (total: 28.6s)

sample272.0ms

Algorithm
intervals
Results
99.0ms361×body80nan
22.0ms182×body80valid
15.0ms27×body640valid
14.0ms23×body1280valid
11.0ms19×body1280nan
7.0ms15×body640nan
6.0ms13×body320valid
3.0ms11×body320nan
2.0ms11×body160valid
1.0ms4×body160nan

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01827
13927
29327
319827
443227
577727
6136727
7354627
done500027

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize38.0ms

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)
11.0b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite200.0ms

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:
77.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
18.0ms
(* (sqrt 2.0) t)
30.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
71.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series3.0s

Counts
4 → 12
Calls
4 calls:
696.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
72.0ms
(* (sqrt 2.0) t)
337.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.9s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.9s

Counts
92 → 92
Iterations

Useful iterations: 2 (483.0ms)

IterNodesCost
01682472
14572291
226272087
done50002087

prune486.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.1b

localize35.0ms

Local error

Found 4 expressions with local error:

3.9b
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
4.7b
(/ (pow l 2) x)
11.3b
(/ (pow t 2) x)
27.7b
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

rewrite150.0ms

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-+l+ 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:
33.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
9.0ms
(/ (pow l 2) x)
8.0ms
(/ (pow t 2) x)
90.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
27.0ms
(/ (pow l 2) x)
21.0ms
(/ (pow t 2) x)
414.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

simplify1.7s

Counts
142 → 142
Iterations

Useful iterations: 2 (601.0ms)

IterNodesCost
02542312
15682086
229341875
done50001875

prune672.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
3.9b
(+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x)))
11.3b
(/ (pow t 2) x)
27.7b
(sqrt (+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
12×unpow-prod-down
11×add-exp-log
8×associate-*r/ add-cbrt-cube associate-/l*
7×pow1 sqrt-prod
6×associate-*l* add-log-exp
4×flip3-+ sqrt-div frac-add flip-+ unpow2 sqr-pow
3×div-exp associate-*r* associate-/r*
2×associate-+l+ unswap-sqr
1×cbrt-undiv +-commutative distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down pow-exp prod-exp clear-num sum-log *-commutative cbrt-unprod div-inv
Counts
4 → 103
Calls
4 calls:
21.0ms
(* (sqrt 2.0) t)
41.0ms
(+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x)))
17.0ms
(/ (pow t 2) x)
35.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x))))

series398.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (sqrt 2.0) t)
88.0ms
(+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x)))
26.0ms
(/ (pow t 2) x)
218.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x))))

simplify2.3s

Counts
115 → 115
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02242093
15641851
231171692
done50001688

prune753.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
3.9b
(+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x)))
11.3b
(/ (pow t 2) x)
27.7b
(sqrt (+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x))))

rewrite68.0ms

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-*r/ associate-/l* add-log-exp
6×add-cbrt-cube
5×pow1 flip3-+ flip-+
4×sqrt-div frac-add unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×+-commutative associate-+l+ sum-log
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 92
Calls
4 calls:
8.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
15.0ms
(+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x)))
16.0ms
(/ (pow t 2) x)
26.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
98.0ms
(+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x)))
33.0ms
(/ (pow t 2) x)
239.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x))))

simplify2.2s

Counts
104 → 104
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02102171
15311901
229421732
done50021726

prune684.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

regimes715.0ms

Accuracy

72.4% (6.7b remaining)

Error of 10.4b against oracle of 3.7b and baseline of 28.0b

bsearch1.3s

Steps
ItersRangePoint
9
120598577249.33295
4.0571253922894675e+17
3.996178578621348e+17
7
2.350322407405638e-155
1.4722807743973814e-153
2.3938287644345074e-155
9
1.0833252341973962e-258
2.7305213248627865e-250
4.761463376941263e-255
4
2.4448033833944457e-307
3.792221310577071e-307
2.483283582103816e-307
7
-1.0924451814151017e-167
-1.515188990120532e-169
-2.7475651167318553e-168
8
-2.766418797691212e+17
-341683923293129.4
-2.739099727305944e+17

simplify26.0ms

Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
067228
184211
done84211

end0.0ms

sample6.6s

Algorithm
intervals
Results
2.2s10120×body80nan
791.0ms5129×body80valid
689.0ms835×body1280valid
586.0ms994×body640valid
342.0ms662×body320valid
340.0ms577×body1280nan
284.0ms597×body640nan
149.0ms359×body320nan
82.0ms380×body160valid
76.0ms186×body160nan