Details

sample39.0ms

Algorithm

intervals

Results

13.0ms	283×	body	80	valid
4.0ms	98×	body	80	nan

simplify5.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
3.9b	(* (* x y) z)
10.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite79.0ms

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))
17.0ms	(* (* x y) z)
42.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms	(sqrt (- (* z z) (* t a)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* z z) (* t a))
26.0ms	(* (* x y) z)
100.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
146.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Counts: 88 → 88

prune243.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
2.4b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite85.0ms

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:

14.0ms	(/ z (sqrt (- (* z z) (* t a))))
8.0ms	(- (* z z) (* t a))
49.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
9.0ms	(sqrt (- (* z z) (* t a)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ z (sqrt (- (* z z) (* t a))))
36.0ms	(- (* z z) (* t a))
96.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
69.0ms	(sqrt (- (* z z) (* t a)))

simplify56.0ms

Counts: 124 → 124

prune299.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
0.8b	(- (* z z) (* t a))
1.5b	(* y (/ z (sqrt (- (* z z) (* t a)))))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

47.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
8.0ms	(- (* z z) (* t a))
40.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
15.0ms	(sqrt (- (* z z) (* t a)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
36.0ms	(- (* z z) (* t a))
66.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
68.0ms	(sqrt (- (* z z) (* t a)))

simplify49.0ms

Counts: 104 → 104

prune251.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.8b

localize33.0ms

Local error

Found 4 expressions with local error:

12.7b	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
26.2b	(sqrt (- (* z z) (* t a)))
26.2b	(sqrt (- (* z z) (* t a)))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`associate-*r/`
1×	`cbrt-prod` `cbrt-div` `pow1/3`

Counts

4 → 55

Calls

4 calls:

41.0ms	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
9.0ms	(sqrt (- (* z z) (* t a)))
9.0ms	(sqrt (- (* z z) (* t a)))
9.0ms	(sqrt (- (* z z) (* t a)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
67.0ms	(sqrt (- (* z z) (* t a)))
64.0ms	(sqrt (- (* z z) (* t a)))
67.0ms	(sqrt (- (* z z) (* t a)))

simplify60.0ms

Counts: 67 → 67

prune271.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.8b

regimes410.0ms

Accuracy

87.3% (2.5b remaining)

Error of 6.0b against oracle of 3.5b and baseline of 23.0b

bsearch56.0ms

Steps

Iters	Range		Point
1	2.7753413219507016e+156	2.949286285521596e+156	2.818827562843425e+156
9	-3.285142281572991e+120	-3.2249995708726854e+115	-5.1997141694493184e+116

simplify1.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

572.0ms	8864×	body	80	valid
146.0ms	2951×	body	80	nan