Details

sample36.0ms

Algorithm

intervals

Results

13.0ms	278×	body	80	valid
4.0ms	100×	body	80	nan

simplify134.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	285
1	22	285
2	37	285
3	58	285
4	77	285
5	97	285
6	106	285
done	106	285

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
5.0b	(* (* x y) z)
11.2b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.2b	(sqrt (- (* z z) (* t a)))

rewrite78.0ms

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))
14.0ms	(* (* x y) z)
35.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
19.0ms	(sqrt (- (* z z) (* t a)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* z z) (* t a))
41.0ms	(* (* x y) z)
110.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
83.0ms	(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts

98 → 98

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	146	26392
1	376	23328
2	1480	22968
done	5001	22903

prune674.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize42.0ms

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)))))
27.2b	(sqrt (- (* z z) (* t a)))

rewrite94.0ms

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:

24.0ms	(/ z (sqrt (- (* z z) (* t a))))
13.0ms	(- (* z z) (* t a))
39.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ z (sqrt (- (* z z) (* t a))))
43.0ms	(- (* z z) (* t a))
108.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
83.0ms	(sqrt (- (* z z) (* t a)))

simplify2.8s

Counts

134 → 134

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	178	42931
1	493	38917
2	1819	38674
done	5001	38129

prune960.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.2b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.4b	(* y (/ z (sqrt (- (* z z) (* t a)))))
27.2b	(sqrt (- (* z z) (* t a)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
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×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `div-inv`

Counts

4 → 102

Calls

4 calls:

13.0ms	(- (* z z) (* t a))
50.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
57.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
23.0ms	(sqrt (- (* z z) (* t a)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* z z) (* t a))
103.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
105.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
108.0ms	(sqrt (- (* z z) (* t a)))

simplify2.5s

Counts

114 → 114

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	173	33045
1	441	29574
2	1387	29454
done	5000	29189

prune839.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.4b

localize76.0ms

Local error

Found 4 expressions with local error:

1.2b	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
8.2b	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
28.1b	(cbrt (- (* z z) (* t a)))
28.1b	(cbrt (- (* z z) (* t a)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
34×	`add-cbrt-cube` `associate-r` `add-exp-log`
33×	`*-un-lft-identity` `add-cube-cbrt`
22×	`sqrt-prod`
17×	`cbrt-prod`
16×	`associate-l`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
8×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`cbrt-div`
5×	`associate-*r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `pow1/3` `sqrt-div` `associate-l/` `associate-/r/` `-commutative` `div-inv`

Counts

4 → 135

Calls

4 calls:

80.0ms	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
48.0ms	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
5.0ms	(cbrt (- (* z z) (* t a)))
6.0ms	(cbrt (- (* z z) (* t a)))

series828.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
221.0ms	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
133.0ms	(cbrt (- (* z z) (* t a)))
134.0ms	(cbrt (- (* z z) (* t a)))

simplify3.7s

Counts

147 → 147

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	270	77549
1	784	70833
2	2631	69705
done	5000	69207

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 2.4b

regimes1.2s

Accuracy

84.4% (3.0b remaining)

Error of 6.3b against oracle of 3.3b and baseline of 22.6b

bsearch51.0ms

Steps

Iters	Range		Point
1	1.8047529537396908e+77	1.9106710751339173e+77	1.8841915447853606e+77
9	-1.5609492160219461e+159	-1.6646169640830922e+150	-1.0342362768199871e+154

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	667
1	27	667
2	30	667
done	30	667

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.2s	8886×	body	80	valid
246.0ms	3063×	body	80	nan