Details

sample33.0ms

Algorithm

intervals

Results

14.0ms

282×

body

valid

simplify118.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize13.0ms

Local error

Found 2 expressions with local error:

2.7b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.7b	(* y (+ 1.0 (* z z)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-*r/`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `div-inv`
2×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l/` `unswap-sqr`

Counts

2 → 70

Calls

2 calls:

24.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
17.0ms	(* y (+ 1.0 (* z z)))

series125.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
59.0ms	(* y (+ 1.0 (* z z)))

simplify663.0ms

Counts: 76 → 76

prune206.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
2.7b	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
15.1b	(sqrt (+ 1.0 (* z z)))
15.1b	(sqrt (+ 1.0 (* z z)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-div`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-*r/`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
8×	`frac-times` `associate-/r/`
6×	`associate-r`
4×	`associate-*l/` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

71.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
74.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
8.0ms	(sqrt (+ 1.0 (* z z)))
8.0ms	(sqrt (+ 1.0 (* z z)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
89.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
62.0ms	(sqrt (+ 1.0 (* z z)))
62.0ms	(sqrt (+ 1.0 (* z z)))

simplify1.0s

Counts: 129 → 129

prune430.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.8b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
4.3b	(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
15.1b	(sqrt (+ 1.0 (* z z)))
15.1b	(sqrt (+ 1.0 (* z z)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

299×	`times-frac`
118×	`add-sqr-sqrt`
116×	`add-cube-cbrt` `*-un-lft-identity`
66×	`sqrt-prod`
34×	`add-exp-log` `add-cbrt-cube`
32×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/` `div-inv`
17×	`cbrt-undiv` `div-exp`
16×	`associate-*r/`
11×	`flip3-+` `flip-+`
7×	`associate-/r*`
6×	`pow1`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 240

Calls

4 calls:

53.0ms	(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
25.0ms	(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
8.0ms	(sqrt (+ 1.0 (* z z)))
14.0ms	(sqrt (+ 1.0 (* z z)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
120.0ms	(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
60.0ms	(sqrt (+ 1.0 (* z z)))
57.0ms	(sqrt (+ 1.0 (* z z)))

simplify1.3s

Counts: 252 → 252

prune880.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ 1.0 (* x (* y (+ 1.0 (* z z)))))
2.4b	(* x (* y (+ 1.0 (* z z))))
5.7b	(* y (+ 1.0 (* z z)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `add-sqr-sqrt` `associate-*r/`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down`
3×	`cbrt-undiv` `flip3-+` `times-frac` `div-exp` `flip-+` `associate-/l*` `add-log-exp`
2×	`associate-/r/` `*-commutative`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`

Counts

3 → 71

Calls

3 calls:

23.0ms	(/ 1.0 (* x (* y (+ 1.0 (* z z)))))
28.0ms	(* x (* y (+ 1.0 (* z z))))
16.0ms	(* y (+ 1.0 (* z z)))

series207.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/ 1.0 (* x (* y (+ 1.0 (* z z)))))
71.0ms	(* x (* y (+ 1.0 (* z z))))
73.0ms	(* y (+ 1.0 (* z z)))

simplify699.0ms

Counts: 80 → 80

prune134.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.8b

regimes214.0ms

Accuracy

1.1% (1.6b remaining)

Error of 6.9b against oracle of 5.3b and baseline of 6.9b

bsearch1.0ms

simplify423.0ms

end0.0ms

sample954.0ms

Algorithm

intervals

Results

552.0ms

8620×

body

valid