Details

Time bar (total: 8.9m)

sample1.0s

Algorithm
intervals
Results
520.0ms169×body80valid
68.0ms293×body80nan
31.0ms34×body640valid
30.0ms26×body1280valid
23.0ms18×body1280nan
18.0ms19×body640nan
10.0ms16×body320valid
9.0ms13×body320nan
5.0ms10×body160nan
4.0ms11×body160valid

simplify269.0ms

Calls
1 calls:
Slowest
268.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize55.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.5b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b
(* (sqrt 2) t)
0.0b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite4.5s

Algorithm
rewrite-expression-head
Rules
2006×add-sqr-sqrt
1306×*-un-lft-identity
990×associate-*l*
959×times-frac
720×prod-diff
610×add-cube-cbrt
504×sqrt-prod
413×difference-of-squares
381×unswap-sqr
337×associate-*r*
201×swap-sqr
176×distribute-lft-out
148×*-commutative
140×distribute-lft-out--
64×difference-of-sqr-1
48×fma-neg
34×associate-/r/
25×associate-/r*
19×flip3-- flip--
17×div-inv
16×associate-/l*
11×add-cbrt-cube add-exp-log
7×pow1
6×add-log-exp
4×expm1-log1p-u sqrt-div associate--l+ insert-posit16 log1p-expm1-u
2×distribute-rgt-in cbrt-undiv +-commutative distribute-lft-in div-exp prod-exp cbrt-unprod
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down
Calls
4 calls:
Slowest
1.7s
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.3s
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
15.0ms
(* (sqrt 2) t)

series2.3s

Calls
4 calls:
Slowest
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
474.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
247.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
70.0ms
(* (sqrt 2) t)

simplify7.6m

Calls
2421 calls:
Slowest
1.0s
(fma (/ 1 (+ (sqrt x) 1)) (* (/ (+ x 1) (- (sqrt x) 1)) (+ (* l l) (* 2 (* t t)))) (- (* (sqrt l) (* l (sqrt l)))))
876.0ms
(fma (/ 1 (+ (sqrt x) (sqrt 1))) (* (/ (+ x 1) (- (sqrt x) (sqrt 1))) (+ (* l l) (* 2 (* t t)))) (- (* l l)))
844.0ms
(fma (* (/ (+ x 1) (- x 1)) 1) (+ (* l l) (* 2 (* t t))) (- (* (* (cbrt l) (cbrt l)) (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))))))
834.0ms
(fma (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (+ x 1) (cbrt (- x 1))) (+ (* l l) (* 2 (* t t)))) (- (* l l)))
824.0ms
(fma (/ (sqrt (+ x 1)) (+ (sqrt x) 1)) (* (/ (sqrt (+ x 1)) (- (sqrt x) 1)) (+ (* l l) (* 2 (* t t)))) (- (* (* l l) 1)))

prune22.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.2b

localize45.0ms

Local error

Found 4 expressions with local error:

25.9b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
9.3b
(/ (* (* t t) 4) x)
3.0b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b
(* (sqrt 2) t)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
84×times-frac
78×associate-*l*
65×*-un-lft-identity add-cube-cbrt
30×unswap-sqr
28×associate-/l*
27×associate-*r*
16×swap-sqr
15×add-cbrt-cube add-exp-log
13×*-commutative
7×pow1 sqrt-prod
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* div-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down fma-udef div-inv
Calls
4 calls:
Slowest
34.0ms
(/ (* (* t t) 4) x)
11.0ms
(* (sqrt 2) t)
1.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series699.0ms

Calls
4 calls:
Slowest
501.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
89.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
66.0ms
(* (sqrt 2) t)
42.0ms
(/ (* (* t t) 4) x)

simplify10.8s

Calls
229 calls:
Slowest
445.0ms
(/ (* (* t t) (sqrt 4)) (* (cbrt x) (cbrt x)))
389.0ms
(/ (* (* t t) (* (cbrt 4) (cbrt 4))) (* (cbrt x) (cbrt x)))
264.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
243.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
229.0ms
(/ (* (* t t) (* (cbrt 4) (cbrt 4))) 1)

prune3.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize34.0ms

Local error

Found 4 expressions with local error:

25.9b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
9.3b
(/ (* (* t t) 4) x)
3.0b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
392×add-sqr-sqrt
195×unswap-sqr
162×cbrt-prod
133×associate-*l*
84×times-frac sqrt-prod
80×*-un-lft-identity add-cube-cbrt
56×associate-*r*
48×add-cbrt-cube
47×swap-sqr
40×cbrt-unprod
28×associate-/l*
25×add-exp-log
19×*-commutative
17×pow1
11×prod-exp
8×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* div-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef div-inv
Calls
4 calls:
Slowest
78.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
68.0ms
(/ (* (* t t) 4) x)
3.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series745.0ms

Calls
4 calls:
Slowest
504.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
109.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
79.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
52.0ms
(/ (* (* t t) 4) x)

simplify24.5s

Calls
433 calls:
Slowest
979.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* t t) t)))
491.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* t t) t)))
476.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* t t) t)))
462.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
451.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* t t) t)))

prune5.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

25.9b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
9.3b
(/ (* (* t t) 4) x)
3.0b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) t))

rewrite830.0ms

Algorithm
rewrite-expression-head
Rules
13002×add-sqr-sqrt
11219×cbrt-prod
9432×unswap-sqr
3200×sqrt-prod
1408×swap-sqr
685×associate-*l*
328×cbrt-unprod
270×add-cbrt-cube
269×*-commutative
131×associate-*r*
109×add-cube-cbrt
99×*-un-lft-identity
84×times-frac
54×add-exp-log
46×pow1
34×prod-exp
31×pow-prod-down
28×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* div-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef div-inv
Calls
4 calls:
Slowest
462.0ms
(* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) t))
52.0ms
(/ (* (* t t) 4) x)
1.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series757.0ms

Calls
4 calls:
Slowest
558.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
97.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
71.0ms
(* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) t))
31.0ms
(/ (* (* t t) 4) x)