Details

sample43.0ms

Algorithm

intervals

Results

17.0ms	281×	body	80	valid
4.0ms	63×	body	80	nan

simplify17.0ms

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

prune4.0ms

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: 26.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
4.3b	(* (* x y) z)
8.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.5b	(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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:

7.0ms	(- (* 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)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) z)
108.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
73.0ms	(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (60.0ms)

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

prune243.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	9	89

Merged error: 2.9b

Counts

89 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
5.3b	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
26.4b	(cbrt (- (* z z) (* t a)))
26.4b	(cbrt (- (* z z) (* t a)))

rewrite65.0ms

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:

7.0ms	(/ 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)))
4.0ms	(cbrt (- (* z z) (* t a)))

series667.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
383.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
109.0ms	(cbrt (- (* z z) (* t a)))
112.0ms	(cbrt (- (* z z) (* t a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1081	3457
1	5001	3199

prune840.0ms

Filtered

221 candidates to 182 candidates (82.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	218	3	221
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	219	11	230

Merged error: 2.9b

Counts

230 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))))
25.5b	(sqrt (- (* z z) (* t a)))
25.5b	(sqrt (- (* z z) (* t a)))
26.4b	(cbrt (- (* z z) (* t a)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
82×	`add-sqr-sqrt`
50×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l`
25×	`add-exp-log` `add-cbrt-cube`
24×	`sqrt-div` `associate-r`
14×	`cbrt-div`
12×	`sqrt-prod`
9×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r/` `flip--` `unswap-sqr`
8×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`frac-times` `div-inv`
4×	`add-log-exp`
3×	`cbrt-prod` `associate-r/` `associate-l/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3` `pow-prod-down` `*-commutative`

Counts

4 → 144

Calls

4 calls:

39.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))))
5.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))))
79.0ms	(sqrt (- (* z z) (* t a)))
80.0ms	(sqrt (- (* z z) (* t a)))
113.0ms	(cbrt (- (* z z) (* t a)))

simplify131.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	947	2715
1	3925	2413
2	5001	2403

prune728.0ms

Filtered

156 candidates to 133 candidates (85.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	156	11	167

Merged error: 2.9b

Counts

167 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (/ x (/ (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
25.5b	(sqrt (- (* z z) (* t a)))
25.5b	(sqrt (- (* z z) (* t a)))
26.4b	(cbrt (- (* z z) (* t a)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
108×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l`
33×	`associate-r`
30×	`sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
15×	`cbrt-prod`
12×	`unswap-sqr`
9×	`cbrt-undiv` `div-exp`
8×	`pow1`
6×	`sqrt-div` `prod-exp` `cbrt-unprod`
5×	`div-inv`
4×	`cbrt-div` `flip3--` `flip--` `add-log-exp`
3×	`associate-/r/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 156

Calls

4 calls:

38.0ms	(* (/ x (/ (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
5.0ms	(sqrt (- (* z z) (* t a)))
5.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series671.0ms

Counts

4 → 12

Calls

4 calls:

415.0ms	(* (/ x (/ (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
79.0ms	(sqrt (- (* z z) (* t a)))
74.0ms	(sqrt (- (* z z) (* t a)))
103.0ms	(cbrt (- (* z z) (* t a)))

simplify138.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	976	3459
1	4098	3158
2	5002	3148

prune727.0ms

Filtered

168 candidates to 136 candidates (81.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	168	11	179

Merged error: 2.9b

Counts

179 → 11

regimes631.0ms

Accuracy

80% (4.3b remaining)

Error of 7.6b against oracle of 3.3b and baseline of 24.7b

bsearch104.0ms

Steps

Iters	Range		Point
8	2.0803801984952915e+82	5.581089211160368e+85	2.772725218861142e+83
6	-9.287529331322677e+113	-1.109941606813071e+113	-1.1283768479081667e+113

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	24
1	38	24
2	38	24

end0.0ms

sample828.0ms

Algorithm

intervals

Results

366.0ms	8863×	body	80	valid
105.0ms	2803×	body	80	nan