Details

sample46.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	9	15
1	23	14
2	52	14
3	115	14
4	249	14
5	516	14
6	1111	14
7	4552	14
done	5000	14

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.2b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite64.0ms

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:

14.0ms	(+ (* x x) (* y y))
49.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series126.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (* x x) (* y y))
89.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify2.2s

Counts

53 → 53

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	95	874
1	352	767
2	2743	639
done	5000	635

prune214.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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

rewrite149.0ms

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:

1.0ms	(hypot x y)
26.0ms	(/ (+ x y) (hypot x y))
89.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
23.0ms	(/ (- x y) (hypot x y))

series413.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(hypot x y)
122.0ms	(/ (+ x y) (hypot x y))
112.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
125.0ms	(/ (- x y) (hypot x y))

simplify2.2s

Counts

158 → 158

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	172	2247
1	509	2185
2	2834	1989
done	5002	1971

prune542.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (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)))
0.0b	(/ (- x y) (hypot x y))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
58×	`times-frac`
41×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-l`
16×	`associate-r`
9×	`associate-/l*`
8×	`cbrt-prod`
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`
3×	`cube-div` `cbrt-div`
2×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`cube-mult` `unpow-prod-down` `flip3--` `flip3-+` `pow1/3` `unpow3` `div-sub` `cube-prod` `pow-prod-down` `*-commutative` `flip--` `rem-cbrt-cube` `flip-+` `sqr-pow`

Counts

4 → 158

Calls

4 calls:

3.0ms	(cbrt (pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3))
19.0ms	(/ (+ x y) (hypot x y))
88.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
38.0ms	(/ (- x y) (hypot x y))

series567.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3))
151.0ms	(/ (+ x y) (hypot x y))
123.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
116.0ms	(/ (- x y) (hypot x y))

simplify2.9s

Counts

170 → 170

Iterations

Useful iterations: 2 (633.0ms)

Iter	Nodes	Cost
0	204	2772
1	623	2454
2	4212	2388
done	5002	2388

prune843.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

38.0ms	(pow (/ (* (- x y) (/ (+ x y) (hypot x y))) (hypot x y)) 3)
8.0ms	(cbrt (pow (/ (* (- x y) (/ (+ x y) (hypot x y))) (hypot x y)) 3))
27.0ms	(/ (+ x y) (hypot x y))
70.0ms	(* (- x y) (/ (+ x y) (hypot x y)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (/ (* (- x y) (/ (+ x y) (hypot x y))) (hypot x y)) 3)
169.0ms	(cbrt (pow (/ (* (- x y) (/ (+ x y) (hypot x y))) (hypot x y)) 3))
124.0ms	(/ (+ x y) (hypot x y))
133.0ms	(* (- x y) (/ (+ x y) (hypot x y)))

simplify3.2s

Counts

162 → 162

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	197	2932
1	605	2636
2	4420	2380
done	5000	2380

prune532.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes52.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18
done	13	18

end0.0ms

sample938.0ms

Algorithm

intervals

Results

525.0ms	8000×	body	80	valid
145.0ms	8000×	pre	80	true