Details

Time bar (total: 19.3s)

sample27.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
5.0ms256×pre80true

simplify7.2s

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
0915
12314
25214
311314
422914
546114
682214
7130814
8329614
done500014

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.2b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
18.4b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/l/
7×add-exp-log add-cbrt-cube
5×flip3-+ flip-+
4×add-sqr-sqrt frac-times add-cube-cbrt *-un-lft-identity add-log-exp
3×flip3-- times-frac associate-/r* flip--
2×pow1 cbrt-undiv expm1-log1p-u associate-*r/ div-exp associate-*l/ associate-/r/ log1p-expm1-u
1×+-commutative fma-def frac-2neg prod-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
2 → 47
Calls
2 calls:
18.0ms
(+ (* x x) (* y y))
72.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series170.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(+ (* x x) (* y y))
126.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.2s

Counts
53 → 53
Iterations

Useful iterations: done (1.2s)

IterNodesCost
095874
1317764
21517635
done5000627

prune238.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ x y) (hypot x y))
0.0b
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
0.0b
(/ (- x y) (hypot x y))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
67×*-un-lft-identity
65×add-sqr-sqrt
58×times-frac
39×add-cube-cbrt
19×add-exp-log associate-*l* add-cbrt-cube
16×associate-*r*
9×associate-/l*
7×distribute-lft-out distribute-lft-out-- difference-of-squares
6×cbrt-undiv div-exp associate-/r*
5×pow1
4×prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×frac-times flip3-- flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+
Counts
3 → 136
Calls
3 calls:
19.0ms
(/ (+ x y) (hypot x y))
58.0ms
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
36.0ms
(/ (- x y) (hypot x y))

series444.0ms

Counts
3 → 9
Calls
3 calls:
150.0ms
(/ (+ x y) (hypot x y))
142.0ms
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
151.0ms
(/ (- x y) (hypot x y))

simplify1.6s

Counts
145 → 145
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01672187
14722127
216441919
done50001918

prune448.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
0.0b
(/ (- x y) (hypot x y))
0.0b
(/ (- x y) (hypot x y))
0.0b
(/ (- x y) (hypot x y))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
93×add-sqr-sqrt
87×*-un-lft-identity
76×times-frac
51×add-cube-cbrt
22×add-exp-log add-cbrt-cube
19×associate-*l*
16×associate-*r*
15×associate-/l* distribute-lft-out-- difference-of-squares
9×associate-/r*
7×cbrt-undiv div-exp
6×pow1 associate-/l/
5×div-inv
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- frac-2neg div-sub clear-num flip-- distribute-lft-out
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 181
Calls
4 calls:
76.0ms
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
23.0ms
(/ (- x y) (hypot x y))
20.0ms
(/ (- x y) (hypot x y))
37.0ms
(/ (- x y) (hypot x y))

series569.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
108.0ms
(/ (- x y) (hypot x y))
166.0ms
(/ (- x y) (hypot x y))
171.0ms
(/ (- x y) (hypot x y))

simplify1.5s

Counts
193 → 193
Iterations

Useful iterations: 2 (370.0ms)

IterNodesCost
01472787
14372709
215412473
done50002473

prune896.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (hypot x y))
0.7b
(cbrt (+ x y))
0.7b
(cbrt (+ x y))
0.7b
(cbrt (+ x y))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
14×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ flip-+ distribute-lft-out
Counts
4 → 61
Calls
4 calls:
2.0ms
(cbrt (hypot x y))
8.0ms
(cbrt (+ x y))
8.0ms
(cbrt (+ x y))
8.0ms
(cbrt (+ x y))

series790.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(cbrt (hypot x y))
164.0ms
(cbrt (+ x y))
197.0ms
(cbrt (+ x y))
259.0ms
(cbrt (+ x y))

simplify3.2s

Counts
73 → 73
Iterations

Useful iterations: done (3.2s)

IterNodesCost
078631
1160594
2331562
3740547
42043547
done5000541

prune534.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes2.0ms