Details

Time bar (total: 9.9m)

sample96.0ms

Algorithm
intervals
Results
39.0ms57×body1280valid
21.0ms43×body640valid
13.0ms128×body80valid
6.0ms17×body320valid
2.0ms11×body160valid

simplify141.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
141.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize16.0ms

Local error

Found 3 expressions with local error:

2.9b
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
0.0b
(/ 2 (+ 1 (exp (* -2 x))))
0.0b
(+ 1 (exp (* -2 x)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
101×*-un-lft-identity
74×add-sqr-sqrt
63×times-frac add-cube-cbrt
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
8×add-exp-log
7×add-log-exp
6×flip3-+ flip-+
5×add-cbrt-cube div-inv
4×associate-/r* difference-of-squares
3×expm1-log1p-u pow1 fma-def insert-posit16 log1p-expm1-u associate-/l*
2×expm1-def difference-of-sqr-1 div-exp
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 150
Calls
3 calls:
Slowest
96.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
10.0ms
(/ 2 (+ 1 (exp (* -2 x))))
9.0ms
(+ 1 (exp (* -2 x)))

series126.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
85.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
24.0ms
(/ 2 (+ 1 (exp (* -2 x))))
16.0ms
(+ 1 (exp (* -2 x)))

simplify28.2s

Counts
230 → 159
Calls
230 calls:
Slowest
628.0ms
(- (* 1 1) (* (exp (* -2 x)) (exp (* -2 x))))
562.0ms
(/ 2 (- (* 1 1) (* (exp (* -2 x)) (exp (* -2 x)))))
513.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
489.0ms
(* (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (/ 2 (+ 1 (exp (* -2 x)))))
401.0ms
(- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

3.0b
(log (exp (- (/ 2 (+ 1 (exp (* -2 x)))) 1)))
2.9b
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
0.0b
(/ 2 (+ 1 (exp (* -2 x))))
0.0b
(+ 1 (exp (* -2 x)))

rewrite330.0ms

Algorithm
rewrite-expression-head
Rules
168×*-un-lft-identity
130×add-sqr-sqrt
108×prod-diff add-cube-cbrt
102×times-frac
59×log-prod
56×exp-sum
26×distribute-lft-out
18×fma-neg
16×associate-/r/
11×log-pow
10×exp-prod
9×flip3-+ add-exp-log flip-+
8×div-inv add-log-exp difference-of-squares
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u associate-/r* difference-of-sqr-1 insert-posit16 log1p-expm1-u
3×fma-def associate-/l*
2×expm1-def sub-neg div-exp distribute-lft-out--
1×cbrt-undiv +-commutative log-div clear-num sum-log frac-2neg flip3-- exp-diff diff-log rem-log-exp flip--
Counts
4 → 232
Calls
4 calls:
Slowest
177.0ms
(log (exp (- (/ 2 (+ 1 (exp (* -2 x)))) 1)))
112.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
21.0ms
(/ 2 (+ 1 (exp (* -2 x))))
11.0ms
(+ 1 (exp (* -2 x)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(log (exp (- (/ 2 (+ 1 (exp (* -2 x)))) 1)))
69.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
29.0ms
(/ 2 (+ 1 (exp (* -2 x))))
17.0ms
(+ 1 (exp (* -2 x)))

simplify51.7s

Counts
374 → 244
Calls
374 calls:
Slowest
675.0ms
(- (* 1 1) (* (exp (* -2 x)) (exp (* -2 x))))
626.0ms
(/ 2 (- (* 1 1) (* (exp (* -2 x)) (exp (* -2 x)))))
571.0ms
(* (cbrt (log (exp (- (/ 2 (+ 1 (exp (* -2 x)))) 1)))) (cbrt (log (exp (- (/ 2 (+ 1 (exp (* -2 x)))) 1)))))
474.0ms
(log (exp (fma (/ (* (cbrt 2) (cbrt 2)) (* (cbrt (+ 1 (exp (* -2 x)))) (cbrt (+ 1 (exp (* -2 x)))))) (/ (cbrt 2) (cbrt (+ 1 (exp (* -2 x))))) (- (* (sqrt 1) (sqrt 1))))))
462.0ms
(- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))

prune2.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

15.4b
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
0.3b
(* x -1/3)
0.0b
(fma 2/15 (pow x 5) x)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 43
Calls
3 calls:
Slowest
6.0ms
(* x -1/3)
0.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
0.0ms
(fma 2/15 (pow x 5) x)

series324.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
198.0ms
(fma 2/15 (pow x 5) x)
107.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
19.0ms
(* x -1/3)

simplify4.1s

Counts
52 → 52
Calls
52 calls:
Slowest
523.0ms
(* (cbrt (fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))) (cbrt (fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))))
519.0ms
(* (cbrt (fma 2/15 (pow x 5) x)) (cbrt (fma 2/15 (pow x 5) x)))
409.0ms
(* (* (fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x)) (fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))) (fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x)))
208.0ms
(* (* (fma 2/15 (pow x 5) x) (fma 2/15 (pow x 5) x)) (fma 2/15 (pow x 5) x))
199.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))

prune493.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

3.0b
(log (exp (- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)))
2.9b
(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)
0.5b
(/ 2 (sqrt (+ 1 (exp (* -2 x)))))
0.0b
(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))

rewrite641.0ms

Algorithm
rewrite-expression-head
Rules
2790×times-frac
2453×*-un-lft-identity
1767×add-sqr-sqrt
1651×add-cube-cbrt
1598×sqrt-prod
1170×prod-diff
590×log-prod
587×exp-sum
392×distribute-lft-out
195×fma-neg
132×sqrt-div associate-/r/
66×flip3-+ flip-+ div-inv
30×associate-/l*
28×difference-of-squares
26×log-pow
25×exp-prod
17×add-exp-log
14×associate-/r* difference-of-sqr-1
11×add-cbrt-cube
7×div-exp
6×add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u
3×expm1-def
2×clear-num sub-neg frac-2neg distribute-lft-out--
1×log-div flip3-- exp-diff diff-log rem-log-exp flip-- associate-/l/
Counts
4 → 1739
Calls
4 calls:
Slowest
317.0ms
(log (exp (- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)))
168.0ms
(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)
31.0ms
(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))
12.0ms
(/ 2 (sqrt (+ 1 (exp (* -2 x)))))

series267.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(log (exp (- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)))
79.0ms
(/ 2 (sqrt (+ 1 (exp (* -2 x)))))
77.0ms
(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)
23.0ms
(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))

simplify8.4m

Counts
3158 → 1751
Calls
3158 calls:
Slowest
964.0ms
(log (exp (fma (/ (/ (sqrt 2) (sqrt (sqrt (+ 1 (exp (* -2 x)))))) (sqrt (sqrt (+ 1 (exp (* -2 x)))))) (/ (/ (sqrt 2) (sqrt (sqrt (+ 1 (exp (* -2 x)))))) (sqrt (sqrt (+ 1 (exp (* -2 x)))))) (- (* 1 1)))))
905.0ms
(fma (/ (/ (* (cbrt 2) (cbrt 2)) (sqrt (sqrt (+ 1 (exp (* -2 x)))))) 1) (/ (/ (cbrt 2) (sqrt (sqrt (+ 1 (exp (* -2 x)))))) (sqrt (+ 1 (exp (* -2 x))))) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))
860.0ms
(log (exp (fma (/ (/ (* (cbrt 2) (cbrt 2)) (sqrt (sqrt (+ 1 (exp (* -2 x)))))) (* (cbrt (sqrt (+ 1 (exp (* -2 x))))) (cbrt (sqrt (+ 1 (exp (* -2 x))))))) (/ (/ (cbrt 2) (sqrt (sqrt (+ 1 (exp (* -2 x)))))) (cbrt (sqrt (+ 1 (exp (* -2 x)))))) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))))
856.0ms
(log (exp (fma (/ 2 (* (cbrt (sqrt (+ 1 (exp (* -2 x))))) (cbrt (sqrt (+ 1 (exp (* -2 x))))))) (/ (/ 1 (sqrt (+ 1 (exp (* -2 x))))) (cbrt (sqrt (+ 1 (exp (* -2 x)))))) (- (* (sqrt 1) (sqrt 1))))))
790.0ms
(fma (/ (/ (sqrt 2) (sqrt (sqrt (+ 1 (exp (* -2 x)))))) (sqrt 1)) (/ (/ (sqrt 2) (sqrt (sqrt (+ 1 (exp (* -2 x)))))) (sqrt (+ 1 (exp (* -2 x))))) (- (* (sqrt 1) (sqrt 1))))