Details

sample53.0ms

Algorithm

intervals

Results

19.0ms	287×	body	80	valid
4.0ms	86×	body	80	nan

simplify104.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	22	14
2	46	14
3	73	14
4	98	14
5	119	14
done	119	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
9.5b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite108.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-l` `prod-diff` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

16.0ms	(- (* z z) (* t a))
19.0ms	(* (* x y) z)
53.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
16.0ms	(sqrt (- (* z z) (* t a)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* z z) (* t a))
33.0ms	(* (* x y) z)
120.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
90.0ms	(sqrt (- (* z z) (* t a)))

simplify1.3s

Counts

98 → 98

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	146	1331
1	386	1225
2	2265	1080
done	5000	1077

prune625.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
3.4b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite117.0ms

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×	`expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-r/` `associate-l` `prod-diff` `clear-num` `-commutative`

Counts

4 → 122

Calls

4 calls:

19.0ms	(/ z (sqrt (- (* z z) (* t a))))
10.0ms	(- (* z z) (* t a))
66.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
18.0ms	(sqrt (- (* z z) (* t a)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ z (sqrt (- (* z z) (* t a))))
43.0ms	(- (* z z) (* t a))
157.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
96.0ms	(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts

134 → 134

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	179	2135
1	497	1953
2	3215	1754
done	5000	1749

prune794.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.8b	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
2.1b	(* x (/ z (sqrt (- (* z z) (* t a)))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite176.0ms

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×	`expm1-log1p-u` `sqrt-div` `pow-prod-down` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `div-inv`

Counts

4 → 102

Calls

4 calls:

15.0ms	(- (* z z) (* t a))
97.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
47.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* z z) (* t a))
141.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
70.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
89.0ms	(sqrt (- (* z z) (* t a)))

simplify974.0ms

Counts

114 → 114

Iterations

Useful iterations: done (972.0ms)

Iter	Nodes	Cost
0	174	1680
1	459	1563
2	1905	1354
done	5000	1353

prune655.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 1.3b

localize37.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (/ (* x y) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
23.0b	(sqrt (- (* z z) (* t a)))
23.0b	(sqrt (- (* z z) (* t a)))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
41×	`add-sqr-sqrt`
33×	`associate-r`
32×	`add-cbrt-cube`
31×	`times-frac`
27×	`add-cube-cbrt` `*-un-lft-identity`
20×	`cbrt-prod` `sqrt-div`
19×	`sqrt-prod`
18×	`prod-exp` `cbrt-unprod`
14×	`cbrt-div`
13×	`cbrt-undiv` `div-exp` `associate-l`
10×	`flip3--` `associate-/r/` `flip--`
9×	`pow1`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 135

Calls

4 calls:

291.0ms	(* (/ (* x y) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
19.0ms	(sqrt (- (* z z) (* t a)))
20.0ms	(sqrt (- (* z z) (* t a)))
24.0ms	(sqrt (- (* z z) (* t a)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (/ (* x y) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
90.0ms	(sqrt (- (* z z) (* t a)))
71.0ms	(sqrt (- (* z z) (* t a)))
105.0ms	(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts

147 → 147

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	222	4530
1	696	4195
2	4172	3262
done	5000	3259

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 1.3b

regimes1.1s

Accuracy

86% (2.6b remaining)

Error of 6.2b against oracle of 3.6b and baseline of 22.4b

bsearch324.0ms

Steps

Iters	Range		Point
9	1.3024678837784223e+151	3.1155849420069337e+159	1.899516655368928e+151
9	1.4441562951991197e-158	2.090050019546481e-149	1.4712586395203132e-158
10	-3.974525488945613e-144	-1.9991754210122156e-159	-1.0822607093553684e-157
10	-3.614756268483021e+161	-1.626953607814572e+151	-2.583745131217405e+153

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	65
1	40	65
2	44	65
done	44	65

end0.0ms

sample2.2s

Algorithm

intervals

Results

658.0ms	8822×	body	80	valid
254.0ms	3000×	body	80	nan