Details

sample21.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify127.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
4.2b	(- (* x x) (* (* y 4.0) y))
30.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

17.0ms	(+ (* x x) (* (* y 4.0) y))
8.0ms	(- (* x x) (* (* y 4.0) y))
28.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (* x x) (* (* y 4.0) y))
46.0ms	(- (* x x) (* (* y 4.0) y))
70.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify2.3s

Counts: 64 → 64

prune163.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
22.4b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
22.4b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt` `associate-/r/` `add-log-exp`
7×	`times-frac`
6×	`associate-/r*`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`pow1` `prod-exp` `cbrt-unprod` `div-inv`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `clear-num` `associate-/l*` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 79

Calls

4 calls:

9.0ms	(+ (* x x) (* (* y 4.0) y))
91.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
43.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
30.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* x x) (* (* y 4.0) y))
108.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
81.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
61.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify830.0ms

Counts: 91 → 91

prune251.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
0.0b	(cbrt (pow (- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))) 3))
22.4b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
22.4b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`add-exp-log` `add-cbrt-cube`
17×	`*-un-lft-identity`
16×	`associate-/r/`
11×	`add-cube-cbrt`
9×	`unpow-prod-down` `distribute-rgt-out--` `times-frac` `cube-prod`
8×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/r*` `add-log-exp` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `cube-div` `cbrt-div` `prod-exp` `cbrt-unprod`
3×	`distribute-lft-out--`
2×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `associate-/l*` `sub-div`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 105

Calls

4 calls:

118.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
151.0ms	(cbrt (pow (- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))) 3))
47.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
30.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
79.0ms	(cbrt (pow (- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))) 3))
57.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
61.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify775.0ms

Counts: 117 → 117

prune323.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify14.0ms

Counts: 0 → 0

prune0.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes171.0ms

Accuracy

60.2% (12.4b remaining)

Error of 12.8b against oracle of 0.3b and baseline of 31.6b

bsearch112.0ms

Steps

Iters	Range		Point
10	8.797133943776216e+194	9.285299668954055e+204	1.2306416332929646e+201
8	5.1891922878729e-207	1.6599456791609415e-203	8.384919188504056e-205
5	9.025940263308786e-273	2.1470355256945754e-272	1.5496305753732154e-272
0	0.0	1.2020271317365e-318	6.0101109554004e-319

simplify633.0ms

end0.0ms

sample742.0ms

Algorithm

intervals

Results

484.0ms

8000×

body

valid