Details

sample44.0ms

Algorithm

intervals

Results

15.0ms	285×	body	80	valid
4.0ms	76×	body	80	nan

simplify43.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	14
1	21	14
2	44	14
3	65	14
4	89	14
5	102	14
done	102	14

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 29.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
6.3b	(* (* x y) z)
9.7b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
28.2b	(sqrt (- (* z z) (* t a)))

rewrite25.0ms

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:

4.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
10.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
33.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
18.0ms	(sqrt (- (* z z) (* t a)))

simplify449.0ms

Counts

88 → 88

Iterations

Useful iterations: done (446.0ms)

Iter	Nodes	Cost
0	134	1237
1	347	1147
2	1653	999
done	5001	978

prune155.0ms

Filtered

61 candidates to 88 candidates (-44.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 5.3b

Counts

89 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
3.5b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
28.2b	(sqrt (- (* z z) (* t a)))

rewrite35.0ms

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×	`flip3--` `associate-/r/` `flip--`
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` `diff-log` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 112

Calls

4 calls:

7.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(- (* z z) (* t a))
16.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ z (sqrt (- (* z z) (* t a))))
8.0ms	(- (* z z) (* t a))
33.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify497.0ms

Counts

124 → 124

Iterations

Useful iterations: done (494.0ms)

Iter	Nodes	Cost
0	166	2031
1	439	1871
2	1752	1679
done	5000	1663

prune142.0ms

Filtered

83 candidates to 124 candidates (-49.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Merged error: 4.8b

Counts

135 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.8b	(* y (/ z (sqrt (- (* z z) (* t a)))))
28.2b	(sqrt (- (* z z) (* t a)))

rewrite38.0ms

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×	`sqrt-div` `pow-prod-down`
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` `diff-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
15.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
12.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
33.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
20.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify1.2s

Counts

104 → 104

Iterations

Useful iterations: 3 (534.0ms)

Iter	Nodes	Cost
0	161	1572
1	400	1468
2	1337	1262
3	4866	1248
done	5000	1248

prune140.0ms

Filtered

72 candidates to 104 candidates (-44.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	104	9	113

Merged error: 4.8b

Counts

113 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(* x (* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))))
1.8b	(* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
29.1b	(cbrt (- (* z z) (* t a)))
29.1b	(cbrt (- (* z z) (* t a)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`cbrt-prod` `cbrt-div` `associate-l`
5×	`associate-*r/`
4×	`cbrt-undiv` `div-exp` `pow-prod-down` `add-log-exp`
3×	`flip3--` `times-frac` `flip--`
2×	`pow1/3` `sqrt-div` `associate-/r/` `*-commutative`
1×	`div-inv` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

13.0ms	(* x (* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))))
13.0ms	(* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
4.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* x (* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))))
67.0ms	(* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
29.0ms	(cbrt (- (* z z) (* t a)))
25.0ms	(cbrt (- (* z z) (* t a)))

simplify652.0ms

Counts

90 → 90

Iterations

Useful iterations: done (649.0ms)

Iter	Nodes	Cost
0	197	2366
1	511	2279
2	1832	1824
done	5001	1796

prune113.0ms

Filtered

68 candidates to 90 candidates (-32.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Merged error: 4.8b

Counts

99 → 9

regimes865.0ms

Accuracy

80.5% (3.9b remaining)

Error of 7.4b against oracle of 3.6b and baseline of 23.4b

bsearch57.0ms

Steps

Iters	Range		Point
7	2.3885905512890262e+30	3.453863445390637e+32	3.362845648801711e+32
8	-4.929111521398201e+98	-1.0818131077010441e+94	-2.2997304670758846e+98

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	40
1	30	40
2	32	40
done	32	40

end0.0ms

sample1.5s

Algorithm

intervals

Results

477.0ms	8938×	body	80	valid
372.0ms	2938×	body	80	nan

Details

sample44.0ms

simplify43.0ms

prune4.0ms

localize11.0ms

rewrite25.0ms

series65.0ms

simplify449.0ms

prune155.0ms

localize11.0ms

rewrite35.0ms

series66.0ms

simplify497.0ms

prune142.0ms

localize11.0ms

rewrite38.0ms

series75.0ms

simplify1.2s

prune140.0ms

localize14.0ms

rewrite37.0ms

series226.0ms

simplify652.0ms

prune113.0ms

regimes865.0ms

bsearch57.0ms

simplify4.0ms

end0.0ms

sample1.5s

Profiling