Details

Time bar (total: 19.9s)

sample337.0ms

Algorithm
intervals
Results
83.0ms26×body640valid
45.0ms299×body80nan
24.0ms168×body80valid
17.0ms24×body1280valid
11.0ms20×body320valid
11.0ms15×body1280nan
10.0ms19×body640nan
7.0ms18×body320nan
5.0ms18×body160valid
2.0ms8×body160nan

simplify6.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01827
13927
29327
318927
439727
566127
6112227
7262427
8413127
done500027

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize46.0ms

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)
13.6b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.4b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite221.0ms

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:
65.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
13.0ms
(* (sqrt 2.0) t)
59.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
80.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts
4 → 12
Calls
4 calls:
686.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
61.0ms
(* (sqrt 2.0) t)
342.0ms
(- (* (/ (+ 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

prune471.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize39.0ms

Local error

Found 4 expressions with local error:

5.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
6.7b
(/ (pow t 2) x)
6.7b
(/ (pow l 2) x)
29.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite95.0ms

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:
36.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
10.0ms
(/ (pow t 2) x)
18.0ms
(/ (pow l 2) x)
22.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
26.0ms
(/ (pow t 2) x)
20.0ms
(/ (pow l 2) x)
268.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify1.3s

Counts
142 → 142
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02542317
15352084
217271868
done50001862

prune736.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
5.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
6.7b
(/ (pow t 2) x)
29.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

rewrite106.0ms

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:
17.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
28.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
18.0ms
(/ (pow t 2) x)
38.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

series423.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
87.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
42.0ms
(/ (pow t 2) x)
242.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

simplify1.3s

Counts
104 → 104
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02102163
15031885
217741702
done50001688

prune643.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize45.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
5.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
6.7b
(/ (pow t 2) x)
29.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
34×times-frac
29×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
22×add-exp-log
18×associate-/l*
9×div-exp add-cbrt-cube
8×associate-*r/
6×cbrt-prod add-log-exp sqr-pow
5×pow1
4×flip3-+ sqrt-div frac-add associate-/r* flip-+ unpow2
3×cbrt-undiv pow-to-exp pow-exp prod-exp sqrt-prod
2×associate-+r+ frac-2neg clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log cbrt-unprod
Counts
4 → 120
Calls
4 calls:
18.0ms
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
16.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
9.0ms
(/ (pow t 2) x)
20.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))))))

series595.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
154.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
35.0ms
(/ (pow t 2) x)
245.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))))))

simplify1.8s

Counts
132 → 132
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02863199
16432893
220942178
done50002098

prune934.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

regimes20.0ms