Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	282×	body	80	valid
4.0ms	103×	body	80	nan

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	14
1	22	14
2	45	14
3	68	14
4	92	14
5	105	14
done	105	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
2.9b	(* (* x y) z)
11.4b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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:

3.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
11.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
26.0ms	(* (* x y) z)
80.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify838.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (184.0ms)

Iter	Nodes	Cost
0	146	1331
1	363	1220
2	1643	1062
done	5001	1062

prune305.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
2.5b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite37.0ms

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:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
3.0ms	(- (* z z) (* t a))
19.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ z (sqrt (- (* z z) (* t a))))
32.0ms	(- (* z z) (* t a))
82.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify848.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (270.0ms)

Iter	Nodes	Cost
0	179	2135
1	449	1941
2	1704	1740
done	5000	1740

prune376.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.3b	(* x (/ z (sqrt (- (* z z) (* t a)))))
1.5b	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite51.0ms

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:

3.0ms	(- (* z z) (* t a))
19.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
19.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
5.0ms	(sqrt (- (* z z) (* t a)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
58.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
84.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
57.0ms	(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts

114 → 114

Iterations

Useful iterations: 3 (898.0ms)

Iter	Nodes	Cost
0	174	1680
1	420	1552
2	1238	1342
3	4561	1340
done	5000	1340

prune336.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
1.5b	(* y (* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
23.6b	(sqrt (- (* z z) (* t a)))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

28×	`sqrt-div`
27×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt` `associate-r`
13×	`pow1`
12×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`flip3--` `associate-/r/` `flip--`
6×	`associate-l` `sqrt-prod`
5×	`associate-*r/`
4×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `times-frac` `div-exp` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `-commutative` `unswap-sqr`
1×	`div-inv`

Counts

4 → 97

Calls

4 calls:

54.0ms	(* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
103.0ms	(* y (* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
4.0ms	(sqrt (- (* z z) (* t a)))
7.0ms	(sqrt (- (* z z) (* t a)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
86.0ms	(* y (* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
61.0ms	(sqrt (- (* z z) (* t a)))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify857.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	171	2530
1	414	1641
2	1325	1386
done	5000	1386

prune370.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

regimes322.0ms

Accuracy

83.8% (3.1b remaining)

Error of 6.6b against oracle of 3.5b and baseline of 22.6b

bsearch93.0ms

Steps

Iters	Range		Point
9	1.1514081473628363e+89	6.147715137559524e+97	8.840009572039548e+95
10	-2.167781788999652e+162	-1.4102566258715918e+152	-1.2137296334810365e+154

simplify7.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	20	29
1	28	29
2	30	29
done	30	29

end0.0ms

sample822.0ms

Algorithm

intervals

Results

357.0ms	8878×	body	80	valid
107.0ms	2953×	body	80	nan