Details

sample48.0ms

Algorithm

intervals

Results

26.0ms

424×

body

valid

simplify773.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
3.9b	(- (+ (* x x) (* y y)) (* z z))
21.3b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

14.0ms	(+ (* x x) (* y y))
80.0ms	(- (+ (* x x) (* y y)) (* z z))
126.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series229.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (* x x) (* y y))
53.0ms	(- (+ (* x x) (* y y)) (* z z))
139.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify629.0ms

Counts: 61 → 61

prune216.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
8.0b	(/ (pow z 2) y)
8.1b	(/ (pow x 2) y)

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
49×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
37×	`add-cube-cbrt`
25×	`unpow-prod-down`
16×	`associate-/l*`
13×	`add-exp-log`
9×	`unpow2` `sqr-pow`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`div-exp` `associate-/r*`
5×	`difference-of-squares`
3×	`pow1`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `diff-log` `pow-exp` `clear-num` `frac-sub` `div-inv` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `flip3-+` `associate--l+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

3 → 121

Calls

3 calls:

277.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
12.0ms	(/ (pow z 2) y)
9.0ms	(/ (pow x 2) y)

series106.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
24.0ms	(/ (pow z 2) y)
29.0ms	(/ (pow x 2) y)

simplify667.0ms

Counts: 130 → 130

prune482.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.8b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
0.2b	(* (fabs z) (/ (fabs z) y))
8.1b	(/ (pow x 2) y)

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

34×	`times-frac`
33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `associate-r`
12×	`unpow-prod-down`
10×	`add-cbrt-cube`
8×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`div-exp` `unpow2` `sqr-pow`
3×	`associate-r/` `associate-l` `associate-/r`
2×	`cbrt-undiv` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow-prod-down` `pow-exp` `associate--l+` `clear-num` `sum-log` `*-commutative` `flip--` `flip-+`

Counts

3 → 97

Calls

3 calls:

207.0ms	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
14.0ms	(* (fabs z) (/ (fabs z) y))
9.0ms	(/ (pow x 2) y)

series127.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
33.0ms	(* (fabs z) (/ (fabs z) y))
23.0ms	(/ (pow x 2) y)

simplify680.0ms

Counts: 106 → 106

prune394.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (* (fabs z) (/ (fabs z) y)))
0.2b	(/ (pow x (/ 2 2)) (/ y x))
0.2b	(* (fabs z) (/ (fabs z) y))

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

173×	`times-frac`
100×	`add-sqr-sqrt`
95×	`add-cube-cbrt` `*-un-lft-identity`
42×	`unpow-prod-down`
21×	`add-exp-log`
14×	`sqr-pow`
13×	`associate-r` `associate-/r*` `add-cbrt-cube`
10×	`div-exp` `div-inv`
8×	`add-log-exp`
7×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
3×	`associate-r/` `associate-l*`
2×	`pow-to-exp` `diff-log` `pow-exp` `prod-exp` `frac-sub` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `associate-/r/` `*-commutative` `flip--` `flip-+`

Counts

3 → 178

Calls

3 calls:

443.0ms	(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (* (fabs z) (/ (fabs z) y)))
36.0ms	(/ (pow x (/ 2 2)) (/ y x))
15.0ms	(* (fabs z) (/ (fabs z) y))

series137.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (* (fabs z) (/ (fabs z) y)))
40.0ms	(/ (pow x (/ 2 2)) (/ y x))
36.0ms	(* (fabs z) (/ (fabs z) y))

simplify1.3s

Counts: 187 → 187

prune640.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes624.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.6s

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s

13623×

body

valid