Details

sample44.0ms

Algorithm

intervals

Results

15.0ms	282×	body	80	valid
4.0ms	74×	body	80	nan

simplify85.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* z z) (* t a))
3.7b	(* (* x y) z)
8.8b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite113.0ms

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:

17.0ms	(- (* z z) (* t a))
25.0ms	(* (* x y) z)
59.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms	(sqrt (- (* z z) (* t a)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* z z) (* t a))
37.0ms	(* (* x y) z)
141.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
97.0ms	(sqrt (- (* z z) (* t a)))

simplify796.0ms

Counts: 88 → 88

prune413.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* z z) (* t a))
0.1b	(/ z (sqrt (- (* z z) (* t a))))
2.7b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

20.0ms	(- (* z z) (* t a))
28.0ms	(/ z (sqrt (- (* z z) (* t a))))
72.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
19.0ms	(sqrt (- (* z z) (* t a)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* z z) (* t a))
78.0ms	(/ z (sqrt (- (* z z) (* t a))))
144.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
91.0ms	(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts: 124 → 124

prune482.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
1.0b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.3b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-r` `sqrt-prod`
20×	`add-exp-log` `add-cbrt-cube`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-l` `associate-/r*`
4×	`pow-prod-down` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `associate-r/` `div-exp` `flip--` `associate-/l` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 121

Calls

4 calls:

27.0ms	(/ z (sqrt (- (* z z) (* t a))))
83.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
56.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
19.0ms	(sqrt (- (* z z) (* t a)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ z (sqrt (- (* z z) (* t a))))
111.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
138.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
104.0ms	(sqrt (- (* z z) (* t a)))

simplify839.0ms

Counts: 133 → 133

prune491.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ z (fabs (cbrt (- (* z z) (* t a)))))
2.7b	(* (* x y) (/ (/ z (fabs (cbrt (- (* z z) (* t a))))) (sqrt (cbrt (- (* z z) (* t a))))))
23.7b	(cbrt (- (* z z) (* t a)))
23.7b	(cbrt (- (* z z) (* t a)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

207×	`times-frac`
123×	`associate-r`
117×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
78×	`sqrt-prod`
45×	`cbrt-prod`
27×	`add-exp-log` `add-cbrt-cube`
11×	`div-inv`
9×	`pow1` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`cbrt-div`
4×	`add-log-exp`
3×	`flip3--` `pow-prod-down` `associate-/r` `flip--` `associate-/l`
2×	`pow1/3` `sqrt-div` `associate-/r/`
1×	`frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 200

Calls

4 calls:

12.0ms	(/ z (fabs (cbrt (- (* z z) (* t a)))))
120.0ms	(* (* x y) (/ (/ z (fabs (cbrt (- (* z z) (* t a))))) (sqrt (cbrt (- (* z z) (* t a))))))
11.0ms	(cbrt (- (* z z) (* t a)))
11.0ms	(cbrt (- (* z z) (* t a)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ z (fabs (cbrt (- (* z z) (* t a)))))
318.0ms	(* (* x y) (/ (/ z (fabs (cbrt (- (* z z) (* t a))))) (sqrt (cbrt (- (* z z) (* t a))))))
140.0ms	(cbrt (- (* z z) (* t a)))
156.0ms	(cbrt (- (* z z) (* t a)))

simplify757.0ms

Counts: 212 → 212

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.4b

regimes522.0ms

Accuracy

85% (2.8b remaining)

Error of 6.2b against oracle of 3.4b and baseline of 22.3b

bsearch145.0ms

Steps

Iters	Range		Point
9	1.2360756061829684e+61	5.577560235509612e+69	3.9337274405595834e+69
10	-1.1830883687720765e+147	-1.3847900762690893e+133	-6.566696069284122e+139

simplify4.2s

end0.0ms

sample1.8s

Algorithm

intervals

Results

591.0ms	8799×	body	80	valid
163.0ms	2973×	body	80	nan