Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	9	15
1	23	14
2	51	14
3	97	14
4	206	14
5	402	14
6	733	14
7	1234	14
8	3218	14
done	5000	14

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.3b

localize9.0ms

Local error

Found 1 expressions with local error:

20.3b

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
6×	`add-exp-log` `add-cbrt-cube`
4×	`frac-times` `flip3-+` `flip-+`
3×	`add-sqr-sqrt` `add-cube-cbrt` `flip3--` `-un-lft-identity` `times-frac` `associate-/r` `flip--`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`pow1` `expm1-log1p-u` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

12.0ms

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series65.0ms

Counts

1 → 3

Calls

1 calls:

65.0ms

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify721.0ms

Counts

36 → 36

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	81	692
1	279	613
2	1179	519
done	5000	519

prune92.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
58×	`times-frac`
40×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-l`
16×	`associate-r`
9×	`associate-/l*`
7×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `hypot-udef` `flip3--` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

4 → 146

Calls

4 calls:

0.0ms	(hypot x y)
8.0ms	(/ (+ x y) (hypot x y))
9.0ms	(/ (- x y) (hypot x y))
33.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot x y)
92.0ms	(/ (+ x y) (hypot x y))
92.0ms	(/ (- x y) (hypot x y))
93.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify898.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (330.0ms)

Iter	Nodes	Cost
0	172	2247
1	490	2185
2	1683	1971
done	5000	1971

prune365.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x y) (hypot x y))
0.0b	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)
0.0b	(/ (- x y) (hypot x y))
0.0b	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
58×	`times-frac`
41×	`add-cube-cbrt`
33×	`add-exp-log` `add-cbrt-cube`
19×	`associate-l`
16×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`pow1` `associate-/l*`
8×	`prod-exp` `cbrt-unprod`
7×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/r*`
5×	`pow-exp` `rem-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`cube-div` `pow-unpow`
2×	`frac-times` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `flip3--` `flip3-+` `unpow3` `div-sub` `cube-prod` `*-commutative` `flip--` `flip-+` `sqr-pow`

Counts

4 → 169

Calls

4 calls:

8.0ms	(/ (+ x y) (hypot x y))
10.0ms	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)
9.0ms	(/ (- x y) (hypot x y))
34.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ x y) (hypot x y))
113.0ms	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)
96.0ms	(/ (- x y) (hypot x y))
96.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify985.0ms

Counts

181 → 181

Iterations

Useful iterations: done (980.0ms)

Iter	Nodes	Cost
0	200	2774
1	570	2517
2	2134	2399
done	5000	2363

prune492.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x y) (hypot x y))
0.0b	(pow (log (exp (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))))) 3)
0.0b	(/ (- x y) (hypot x y))
0.0b	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
58×	`times-frac`
43×	`add-cube-cbrt`
21×	`add-exp-log` `add-cbrt-cube`
19×	`associate-l`
16×	`associate-r`
9×	`pow1` `associate-/l*`
7×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `unpow-prod-down` `cube-prod` `div-exp` `associate-/r*` `log-pow` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l/` `unswap-sqr`
3×	`pow-unpow`
2×	`exp-prod` `exp-to-pow` `frac-2neg` `clear-num`
1×	`cube-mult` `frac-times` `pow-to-exp` `flip3--` `pow-pow` `flip3-+` `unpow3` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `*-commutative` `flip--` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 167

Calls

4 calls:

8.0ms	(/ (+ x y) (hypot x y))
3.0ms	(pow (log (exp (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))))) 3)
9.0ms	(/ (- x y) (hypot x y))
30.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ x y) (hypot x y))
108.0ms	(pow (log (exp (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))))) 3)
95.0ms	(/ (- x y) (hypot x y))
96.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify968.0ms

Counts

179 → 179

Iterations

Useful iterations: 2 (399.0ms)

Iter	Nodes	Cost
0	202	3013
1	568	2700
2	1996	2520
done	5000	2520

prune718.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes42.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	15	20
done	15	20

end0.0ms

sample472.0ms

Algorithm

intervals

Results

231.0ms	8000×	body	80	valid
104.0ms	8000×	pre	80	true