Details

sample39.0ms

Algorithm

intervals

Results

13.0ms	289×	body	80	valid
4.0ms	93×	body	80	nan

simplify4.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* z z) (* t a))
5.5b	(* (* x y) z)
9.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.2b	(sqrt (- (* z z) (* t a)))

rewrite103.0ms

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:

12.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) z)
45.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
14.0ms	(sqrt (- (* z z) (* t a)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) z)
112.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
91.0ms	(sqrt (- (* z z) (* t a)))

simplify57.0ms

Counts: 88 → 88

prune310.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.4b	(- (* z z) (* t a))
4.1b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
25.2b	(sqrt (- (* z z) (* t a)))

rewrite80.0ms

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:

32.0ms	(/ (sqrt (- (* z z) (* t a))) z)
8.0ms	(- (* z z) (* t a))
22.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
10.0ms	(sqrt (- (* z z) (* t a)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (sqrt (- (* z z) (* t a))) z)
58.0ms	(- (* z z) (* t a))
122.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
88.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Counts: 144 → 144

prune458.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* z z) (* t a))
1.4b	(- (* z z) (* t a))
25.9b	(cbrt (- (* z z) (* t a)))
25.9b	(cbrt (- (* z z) (* t a)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp`
6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
2×	`sub-neg` `pow1/3` `diff-log`

Counts

4 → 50

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
20.0ms	(- (* z z) (* t a))
10.0ms	(cbrt (- (* z z) (* t a)))
10.0ms	(cbrt (- (* z z) (* t a)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* z z) (* t a))
39.0ms	(- (* z z) (* t a))
139.0ms	(cbrt (- (* z z) (* t a)))
110.0ms	(cbrt (- (* z z) (* t a)))

simplify95.0ms

Counts: 62 → 62

prune378.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.4b	(- (* z z) (* t a))
2.4b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
25.2b	(sqrt (- (* z z) (* t a)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 227

Calls

4 calls:

73.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
13.0ms	(- (* z z) (* t a))
38.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
16.0ms	(sqrt (- (* z z) (* t a)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
40.0ms	(- (* z z) (* t a))
67.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
79.0ms	(sqrt (- (* z z) (* t a)))

simplify74.0ms

Counts: 239 → 239

prune881.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

regimes510.0ms

Accuracy

84.9% (2.9b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 22.1b

bsearch117.0ms

Steps

Iters	Range		Point
9	4.759253695909312e+109	1.8978878420340277e+115	1.358422658795214e+112
9	-3.252543247102e+95	-2.4276545691008814e+89	-1.988498731083228e+94

simplify329.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

617.0ms	8909×	body	80	valid
563.0ms	3035×	body	80	nan