Details

sample25.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify5.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
20.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite89.0ms

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:

17.0ms	(+ (* x x) (* y y))
69.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series173.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(+ (* x x) (* y y))
115.0ms	(/ (* (- 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

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (/ (fma x x (pow y 2)) (+ x y)))
0.0b	(cbrt (pow (/ (- x y) (/ (fma x x (pow y 2)) (+ x y))) 3))
0.0b	(pow (/ (- x y) (/ (fma x x (pow y 2)) (+ x y))) 3)
19.4b	(/ (fma x x (pow y 2)) (+ x y))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

774×	`times-frac`
664×	`*-un-lft-identity`
500×	`add-sqr-sqrt`
318×	`add-cube-cbrt`
196×	`cbrt-prod`
190×	`unpow-prod-down` `cube-prod`
91×	`distribute-lft-out--` `difference-of-squares`
82×	`distribute-lft-out`
59×	`associate-/r/`
32×	`div-inv`
27×	`flip3-+` `flip-+`
22×	`associate-/r*`
17×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-exp` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `frac-2neg` `unpow3` `clear-num` `associate-/l/` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow1/3` `div-sub` `flip--` `rem-cbrt-cube`

Counts

4 → 590

Calls

4 calls:

46.0ms	(/ (- x y) (/ (fma x x (pow y 2)) (+ x y)))
47.0ms	(cbrt (pow (/ (- x y) (/ (fma x x (pow y 2)) (+ x y))) 3))
67.0ms	(pow (/ (- x y) (/ (fma x x (pow y 2)) (+ x y))) 3)
24.0ms	(/ (fma x x (pow y 2)) (+ x y))

series457.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- x y) (/ (fma x x (pow y 2)) (+ x y)))
133.0ms	(cbrt (pow (/ (- x y) (/ (fma x x (pow y 2)) (+ x y))) 3))
125.0ms	(pow (/ (- x y) (/ (fma x x (pow y 2)) (+ x y))) 3)
99.0ms	(/ (fma x x (pow y 2)) (+ x y))

simplify1.2s

Counts

602 → 602

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	513	19160
1	2193	17069
done	5002	15755

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 158

Calls

4 calls:

13.0ms	(cbrt (pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3))
38.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
45.0ms	(pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3)
27.0ms	(/ (hypot x y) (+ x y))

series596.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3))
131.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
152.0ms	(pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3)
144.0ms	(/ (hypot x y) (+ x y))

simplify3.1s

Counts

170 → 170

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	197	3132
1	596	2818
2	4075	2539
done	5000	2539

prune471.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

13×	`cbrt-prod`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div`
1×	`flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 55

Calls

4 calls:

4.0ms	(cbrt (+ x y))
1.0ms	(cbrt (hypot x y))
1.0ms	(cbrt (hypot x y))
2.0ms	(cbrt (hypot x y))

series579.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (+ x y))
130.0ms	(cbrt (hypot x y))
132.0ms	(cbrt (hypot x y))
149.0ms	(cbrt (hypot x y))

simplify861.0ms

Counts

67 → 67

Iterations

Useful iterations: 3 (409.0ms)

Iter	Nodes	Cost
0	78	525
1	161	502
2	486	470
3	1858	457
done	5001	457

prune372.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes57.0ms

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

sample915.0ms

Algorithm

intervals

Results

396.0ms	8000×	body	80	valid
265.0ms	8000×	pre	80	true