Details

Time bar (total: 13.7s)

sample34.0ms

Algorithm
intervals
Results
9.0ms272×body80valid
9.0ms296×body80nan

simplify248.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
078
1138
2257
3447
4657
5887
61057
71267
81497
91567
101717
done1717

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma y (sqrt x) (- 1.0 x))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma y (sqrt x) (- 1.0 x))

series48.0ms

Counts
1 → 3
Calls
1 calls:
48.0ms
(fma y (sqrt x) (- 1.0 x))

simplify1.2s

Counts
13 → 13
Iterations

Useful iterations: 4 (392.0ms)

IterNodesCost
026126
153123
2119109
3312109
41214106
done5000106

prune80.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (- 1.0 x) (* y (sqrt x)))
0.2b
(* y (sqrt x))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×*-un-lft-identity
12×add-cube-cbrt
11×associate-+l+
9×prod-diff
7×add-log-exp
6×associate-*r*
5×fma-def
4×pow1 add-exp-log sqrt-prod add-cbrt-cube
3×associate-*l*
2×expm1-log1p-u sum-log log1p-expm1-u unswap-sqr
1×+-commutative associate-+l- sub-neg flip3-+ diff-log pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out-- difference-of-squares
Counts
2 → 55
Calls
2 calls:
56.0ms
(+ (- 1.0 x) (* y (sqrt x)))
10.0ms
(* y (sqrt x))

series94.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(+ (- 1.0 x) (* y (sqrt x)))
44.0ms
(* y (sqrt x))

simplify3.4s

Counts
61 → 61
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0110620
1273545
2736453
32566429
done5001407

prune175.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt x))
0.1b
(sqrt (sqrt x))
0.2b
(* y (sqrt (sqrt x)))
0.3b
(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
41×sqrt-prod
25×add-sqr-sqrt
18×associate-*r*
15×pow1 add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
8×sqrt-pow1
4×expm1-log1p-u rem-sqrt-square pow1/2 associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×unswap-sqr
2×*-commutative
Counts
4 → 96
Calls
4 calls:
3.0ms
(sqrt (sqrt x))
3.0ms
(sqrt (sqrt x))
17.0ms
(* y (sqrt (sqrt x)))
77.0ms
(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series729.0ms

Counts
4 → 12
Calls
4 calls:
272.0ms
(sqrt (sqrt x))
233.0ms
(sqrt (sqrt x))
148.0ms
(* y (sqrt (sqrt x)))
76.0ms
(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify3.4s

Counts
108 → 108
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0138963
1354754
21000688
33003671
done5001659

prune373.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (sqrt x)))
0.2b
(* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x)))))
0.3b
(* (* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt x)))
0.5b
(* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))

rewrite546.0ms

Algorithm
rewrite-expression-head
Rules
186×sqrt-prod
87×add-sqr-sqrt
81×sqrt-pow1
52×pow1
27×add-cube-cbrt *-un-lft-identity pow1/2
24×swap-sqr
22×associate-*r*
20×add-exp-log add-cbrt-cube
17×unswap-sqr
16×associate-*l* pow-prod-down
13×pow-prod-up
10×prod-exp cbrt-unprod
7×pow-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square *-commutative
1×pow2 pow-plus sqrt-unprod rem-square-sqrt
Counts
4 → 184
Calls
4 calls:
4.0ms
(sqrt (sqrt (sqrt x)))
103.0ms
(* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x)))))
368.0ms
(* (* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt x)))
62.0ms
(* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))

series583.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(sqrt (sqrt (sqrt x)))
96.0ms
(* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x)))))
54.0ms
(* (* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt x)))
201.0ms
(* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))

simplify2.1s

Counts
196 → 196
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02242772
15071311
216021183
done50001160

prune555.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes2.0ms