Details

Time bar (total: 21.2s)

sample492.0ms

Algorithm
intervals
Results
180.0ms24×body1280valid
45.0ms26×body640valid
30.0ms299×body80nan
17.0ms168×body80valid
7.0ms15×body1280nan
7.0ms19×body640nan
6.0ms20×body320valid
5.0ms18×body320nan
4.0ms18×body160valid
1.0ms8×body160nan

simplify4.8s

Counts
1 → 1
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
01827
14126
210026
322426
449726
594126
6155526
7330526
done500126

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize45.0ms

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)))

rewrite204.0ms

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:
60.0ms
(/ (* (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)
31.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
100.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.9s

Counts
4 → 12
Calls
4 calls:
669.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
87.0ms
(* (sqrt 2.0) t)
369.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01792660
14422367
216802178
done50012125

prune615.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

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:
1.0ms
(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
28.0ms
(/ (pow t 2) x)
17.0ms
(/ (pow l 2) x)
3.0ms
(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series543.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
33.0ms
(/ (pow t 2) x)
22.0ms
(/ (pow l 2) x)
380.0ms
(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify2.5s

Counts
139 → 139
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02171761
13761614
29121411
331821411
done50001410

prune748.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b
(fma t t (* l (/ l x)))
5.2b
(fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))
6.7b
(/ (pow t 2) x)
29.0b
(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

rewrite20.0ms

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-/l*
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×div-exp associate-/r* sqrt-prod
2×fma-udef
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
0.0ms
(fma t t (* l (/ l x)))
1.0ms
(fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))
13.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

series625.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(fma t t (* l (/ l x)))
114.0ms
(fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))
20.0ms
(/ (pow t 2) x)
416.0ms
(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

simplify2.0s

Counts
98 → 98
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01591358
12761256
26661108
322891108
done50001107

prune492.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
42×add-sqr-sqrt
40×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×pow1 div-exp associate-/r* sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 132
Calls
4 calls:
9.0ms
(/ (pow t 2) x)
8.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))
2.0ms
(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

series882.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (pow t 2) x)
21.0ms
(/ (pow t 2) x)
403.0ms
(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))
422.0ms
(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

simplify1.6s

Counts
144 → 144
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01331862
12341676
25581492
317861492
done50001490

prune941.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

regimes14.0ms