Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	287×	body	80	valid
5.0ms	112×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	45	7
2	67	7
3	94	7
4	115	7
5	115	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 24.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
4.8b	(* (* x y) z)
8.3b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.0b	(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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:

3.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
10.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
6.0ms	(sqrt (- (* z z) (* t a)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
26.0ms	(* (* x y) z)
84.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	346	584
1	1863	515
2	5002	510

prune221.0ms

Filtered

88 candidates to 60 candidates (68.2%)

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: 3.1b

Counts

89 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
6.4b	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
25.9b	(cbrt (- (* z z) (* t a)))
25.9b	(cbrt (- (* z z) (* t a)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
147×	`add-sqr-sqrt`
102×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l`
33×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
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×	`associate-/r/` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l*`
2×	`pow1/3` `sqrt-div`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 209

Calls

4 calls:

6.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
37.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
4.0ms	(cbrt (- (* z z) (* t a)))
6.0ms	(cbrt (- (* z z) (* t a)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
299.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
80.0ms	(cbrt (- (* z z) (* t a)))
84.0ms	(cbrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1081	3457
1	5001	3199

prune709.0ms

Filtered

221 candidates to 182 candidates (82.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	217	4	221
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	220	12	232

Merged error: 3.1b

Counts

232 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
7.4b	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) z)
25.9b	(cbrt (- (* z z) (* t a)))
25.9b	(cbrt (- (* z z) (* t a)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
93×	`add-sqr-sqrt`
84×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l`
18×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
9×	`div-inv`
6×	`pow1` `cbrt-undiv` `cbrt-prod` `div-exp`
4×	`cbrt-div` `add-log-exp`
3×	`associate-r` `prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`flip3--` `pow1/3` `associate-/r/` `flip--`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 162

Calls

4 calls:

6.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
14.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) z)
3.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
96.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) z)
81.0ms	(cbrt (- (* z z) (* t a)))
83.0ms	(cbrt (- (* z z) (* t a)))

simplify78.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	676	2019
1	2786	1881
2	5001	1875

prune627.0ms

Filtered

174 candidates to 148 candidates (85.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	174	12	186

Merged error: 3.1b

Counts

186 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.8b	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
25.0b	(sqrt (- (* z z) (* t a)))
25.0b	(sqrt (- (* z z) (* t a)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

63×	`sqrt-prod`
48×	`add-sqr-sqrt` `times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
33×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
16×	`sqrt-div`
15×	`associate-l`
9×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r*` `cbrt-unprod`
8×	`pow1`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 141

Calls

4 calls:

9.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
25.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))
7.0ms	(sqrt (- (* z z) (* t a)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
82.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
56.0ms	(sqrt (- (* z z) (* t a)))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify86.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	629	1951
1	3362	1738
2	5001	1614

prune336.0ms

Filtered

153 candidates to 101 candidates (66.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	153	12	165

Merged error: 3.1b

Counts

165 → 12

regimes488.0ms

Accuracy

81.7% (4.1b remaining)

Error of 7.4b against oracle of 3.4b and baseline of 25.6b

bsearch173.0ms

Steps

Iters	Range		Point
10	4.522873592780775e+27	5.978781725101664e+38	4.935646888674816e+38
10	-1.5429529165087941e-18	-2.3261434869364345e-32	-4.59212318019564e-25
8	-4.624215200523427e+124	-2.5454028151105053e+120	-5.143913370988061e+122

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	31
1	45	31
2	45	31

end0.0ms

sample932.0ms

Algorithm

intervals

Results

441.0ms	8841×	body	80	valid
140.0ms	2983×	body	80	nan