Details

sample67.0ms

Algorithm

intervals

Results

21.0ms	291×	body	80	valid
6.0ms	96×	body	80	nan

simplify102.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	118
5	118
4	97
3	72
2	46
1	22
0	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
4.4b	(* (* x y) z)
11.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.1b	(sqrt (- (* z z) (* t a)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
6×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `-commutative` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
26.0ms	(* (* x y) z)
30.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
11.0ms	(sqrt (- (* z z) (* t a)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* z z) (* t a))
38.0ms	(* (* x y) z)
113.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
91.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	2299
1	385
0	146

prune817.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
2.7b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.1b	(sqrt (- (* z z) (* t a)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
24×	`associate-r` `sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
6×	`associate-/r*` `sqrt-div` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `associate-r/` `-commutative`

Counts

4 → 122

Calls

4 calls:

11.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
61.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
17.0ms	(sqrt (- (* z z) (* t a)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ z (sqrt (- (* z z) (* t a))))
53.0ms	(- (* z z) (* t a))
141.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
90.0ms	(sqrt (- (* z z) (* t a)))

simplify2.5s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	3165
1	496
0	179

prune927.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.4b

localize65.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ y (/ (fabs (cbrt (- (* z z) (* t a)))) x))
4.4b	(* (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) x)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
23.8b	(cbrt (- (* z z) (* t a)))
23.8b	(cbrt (- (* z z) (* t a)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
147×	`add-sqr-sqrt`
102×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
33×	`associate-r`
30×	`add-cbrt-cube` `add-exp-log`
24×	`sqrt-prod`
18×	`cbrt-prod`
13×	`associate-/r*`
12×	`cbrt-undiv` `div-exp` `unswap-sqr`
10×	`div-inv`
6×	`pow1` `cbrt-div` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l*`
2×	`pow1/3` `sqrt-div`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 217

Calls

4 calls:

13.0ms	(/ y (/ (fabs (cbrt (- (* z z) (* t a)))) x))
118.0ms	(* (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) x)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
9.0ms	(cbrt (- (* z z) (* t a)))
10.0ms	(cbrt (- (* z z) (* t a)))

series800.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ y (/ (fabs (cbrt (- (* z z) (* t a)))) x))
439.0ms	(* (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) x)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
111.0ms	(cbrt (- (* z z) (* t a)))
155.0ms	(cbrt (- (* z z) (* t a)))

simplify1.4s

Counts

229 → 229

Iterations

Iter	Nodes
done	5000
1	1217
0	386

prune2.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.4b

localize77.0ms

Local error

Found 4 expressions with local error:

23.8b	(cbrt (- (* z z) (* t a)))
23.8b	(cbrt (- (* z z) (* t a)))
23.8b	(cbrt (- (* z z) (* t a)))
23.8b	(cbrt (- (* z z) (* t a)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `pow1/3` `add-exp-log` `log1p-expm1-u` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

5.0ms	(cbrt (- (* z z) (* t a)))
7.0ms	(cbrt (- (* z z) (* t a)))
5.0ms	(cbrt (- (* z z) (* t a)))
5.0ms	(cbrt (- (* z z) (* t a)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (- (* z z) (* t a)))
109.0ms	(cbrt (- (* z z) (* t a)))
127.0ms	(cbrt (- (* z z) (* t a)))
141.0ms	(cbrt (- (* z z) (* t a)))

simplify2.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	2631
2	539
1	160
0	61

prune787.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.4b

regimes1.7s

Accuracy

76.4% (4.6b remaining)

Error of 8.1b against oracle of 3.5b and baseline of 23.0b

bsearch120.0ms

Steps

Iters	Range		Point
5	3.3639079928691005	10.445105708742691	10.242145181597904
7	-6.499354134947939e+42	-2.420896724821489e+41	-6.395336884503867e+42

simplify8.0ms

Iterations

Iter	Nodes
done	44
2	44
1	42
0	31

end0.0ms

sample2.0s

Algorithm

intervals

Results

895.0ms	8830×	body	80	valid
210.0ms	2961×	body	80	nan