Details

Time bar (total: 15.2s)

sample75.0ms

Algorithm
intervals
Results
15.0ms310×body80nan
8.0ms164×body80valid
6.0ms26×body1280valid
6.0ms31×body640valid
4.0ms19×body1280nan
4.0ms20×body640nan
3.0ms20×body320valid
1.0ms11×body320nan
1.0ms15×body160valid
1.0ms6×body160nan

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 42.5b

localize19.0ms

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)
12.6b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.2b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite144.0ms

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:
54.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
9.0ms
(* (sqrt 2.0) t)
29.0ms
(- (* (/ (+ 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:
447.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
41.0ms
(* (sqrt 2.0) t)
222.0ms
(- (* (/ (+ 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)))

simplify885.0ms

Counts
92 → 92
Iterations

Useful iterations: done (881.0ms)

IterNodesCost
01682472
14142283
215522077
done50002025

prune310.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.9b

localize18.0ms

Local error

Found 4 expressions with local error:

3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
5.5b
(/ (pow l 2) x)
10.6b
(/ (pow t 2) x)
29.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite58.0ms

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:
16.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
8.0ms
(/ (pow l 2) x)
8.0ms
(/ (pow t 2) x)
21.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
19.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
168.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify793.0ms

Counts
142 → 142
Iterations

Useful iterations: done (789.0ms)

IterNodesCost
02542317
15352084
217251868
done50011862

prune488.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
10.6b
(/ (pow t 2) x)
29.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

rewrite55.0ms

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-+r+ 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)))
16.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
11.0ms
(/ (pow t 2) x)
18.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

series249.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
53.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
24.0ms
(/ (pow t 2) x)
145.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

simplify796.0ms

Counts
104 → 104
Iterations

Useful iterations: done (789.0ms)

IterNodesCost
02102163
15031885
217741702
done50001688

prune383.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
10.6b
(/ (pow t 2) x)
29.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite55.0ms

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-+r+ 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) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
16.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
11.0ms
(/ (pow t 2) x)
18.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
85.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
19.0ms
(/ (pow t 2) x)
182.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify818.0ms

Counts
104 → 104
Iterations

Useful iterations: done (814.0ms)

IterNodesCost
02002563
14752316
217282084
done50012029

prune372.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

regimes495.0ms

Accuracy

74.2% (6.0b remaining)

Error of 10.2b against oracle of 4.2b and baseline of 27.5b

bsearch637.0ms

Steps
ItersRangePoint
9
1.465138554361753e+145
1.1978127855039438e+150
7.02010337201463e+147
4
8.850619474871086e-234
1.661088650457253e-233
1.4647836581094993e-233
9
4.423936161010146e-305
1.2565912718636627e-298
1.5390966172940503e-299
9
-1.1180435754089893e-220
-2.19452767567629e-228
-7.231141217156239e-225
7
-1.4908441577161578e-155
-6.389616883612984e-157
-6.492099203484522e-157
8
-2.831759546101662e+36
-1.2139019026724813e+32
-2.4046995940459546e+36

simplify16.0ms

Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
070240
189205
292179
395179
done95179

end0.0ms

sample2.2s

Algorithm
intervals
Results
484.0ms10161×body80nan
253.0ms5065×body80valid
205.0ms849×body1280valid
189.0ms1019×body640valid
142.0ms618×body1280nan
113.0ms632×body640nan
94.0ms679×body320valid
46.0ms349×body320nan
36.0ms388×body160valid
16.0ms184×body160nan