Details

sample50.0ms

Algorithm

intervals

Results

17.0ms	283×	body	80	valid
5.0ms	96×	body	80	nan

simplify6.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
4.2b	(* (* x y) z)
10.1b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.8b	(sqrt (- (* z z) (* t a)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
18.0ms	(* (* x y) z)
40.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
30.0ms	(sqrt (- (* z z) (* t a)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* z z) (* t a))
42.0ms	(* (* x y) z)
124.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
90.0ms	(sqrt (- (* z z) (* t a)))

simplify68.0ms

Counts: 88 → 88

prune394.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.0b	(- (* z z) (* t a))
3.6b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.8b	(sqrt (- (* z z) (* t a)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
3×	`flip3--` `flip--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

18.0ms	(/ (sqrt (- (* z z) (* t a))) z)
8.0ms	(- (* z z) (* t a))
51.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms	(sqrt (- (* z z) (* t a)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (sqrt (- (* z z) (* t a))) z)
48.0ms	(- (* z z) (* t a))
147.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
79.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Counts: 144 → 144

prune570.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
1.4b	(* (/ x (sqrt 1)) (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.6b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
23.8b	(sqrt (- (* z z) (* t a)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

308×	`times-frac`
216×	`add-sqr-sqrt`
159×	`*-un-lft-identity`
155×	`add-cube-cbrt`
87×	`sqrt-prod`
71×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
22×	`associate-l` `associate-/r*`
16×	`unswap-sqr`
12×	`cbrt-undiv` `div-exp`
10×	`div-inv`
7×	`pow1`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 266

Calls

4 calls:

14.0ms	(- (* z z) (* t a))
111.0ms	(* (/ x (sqrt 1)) (/ y (/ (sqrt (- (* z z) (* t a))) z)))
30.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
16.0ms	(sqrt (- (* z z) (* t a)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
126.0ms	(* (/ x (sqrt 1)) (/ y (/ (sqrt (- (* z z) (* t a))) z)))
77.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
68.0ms	(sqrt (- (* z z) (* t a)))

simplify48.0ms

Counts: 278 → 278

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ z (sqrt (- (* z z) (* t a)))))
1.0b	(- (* z z) (* t a))
3.6b	(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
23.8b	(sqrt (- (* z z) (* t a)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

473×	`times-frac`
211×	`add-sqr-sqrt`
210×	`add-cube-cbrt` `*-un-lft-identity`
101×	`associate-/r*`
93×	`sqrt-prod`
60×	`add-exp-log`
35×	`div-exp`
30×	`add-cbrt-cube`
24×	`associate-/r/`
22×	`sqrt-div`
15×	`cbrt-undiv`
14×	`div-inv`
12×	`flip3--` `flip--`
7×	`prod-exp`
6×	`pow1` `rec-exp` `1-exp` `add-log-exp`
4×	`associate-/l*`
3×	`cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `inv-pow`

Counts

4 → 333

Calls

4 calls:

33.0ms	(/ 1 (/ z (sqrt (- (* z z) (* t a)))))
14.0ms	(- (* z z) (* t a))
42.0ms	(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
9.0ms	(sqrt (- (* z z) (* t a)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1 (/ z (sqrt (- (* z z) (* t a)))))
37.0ms	(- (* z z) (* t a))
119.0ms	(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
74.0ms	(sqrt (- (* z z) (* t a)))

simplify71.0ms

Counts: 345 → 345

prune1.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.2b

regimes308.0ms

Accuracy

83.4% (3.2b remaining)

Error of 6.8b against oracle of 3.6b and baseline of 22.9b

bsearch101.0ms

Steps

Iters	Range		Point
10	1.4858361027123378e+98	9.96483424774545e+111	7.526056547081697e+111
7	-4.287196334141863e+154	-6.101264141099722e+152	-2.9089074239006997e+153

simplify21.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

882.0ms	8880×	body	80	valid
210.0ms	3001×	body	80	nan