Details

sample53.0ms

Algorithm

intervals

Results

23.0ms	281×	body	80	valid
4.0ms	63×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	46	7
2	72	7
3	99	7
4	120	7
5	120	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: 26.0b

Counts

2 → 1

localize10.0ms

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)))

rewrite23.0ms

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:

4.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
22.0ms	(* (* x y) z)
82.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	368	630
1	1941	560
2	5001	551

prune230.0ms

Filtered

98 candidates to 71 candidates (72.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Merged error: 2.9b

Counts

99 → 9

localize18.0ms

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)))

rewrite55.0ms

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×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `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 → 217

Calls

4 calls:

5.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
32.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
3.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
326.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
105.0ms	(cbrt (- (* z z) (* t a)))
93.0ms	(cbrt (- (* z z) (* t a)))

simplify79.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1093	3523
1	5001	3265

prune964.0ms

Filtered

229 candidates to 190 candidates (83.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	227	11	238

Merged error: 2.9b

Counts

238 → 11

localize18.0ms

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)))

rewrite56.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 152

Calls

4 calls:

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

series505.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))))
60.0ms	(sqrt (- (* z z) (* t a)))
55.0ms	(sqrt (- (* z z) (* t a)))
84.0ms	(cbrt (- (* z z) (* t a)))

simplify100.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	962	2789
1	3976	2487
2	5001	2475

prune683.0ms

Filtered

164 candidates to 141 candidates (86.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	164	11	175

Merged error: 2.9b

Counts

175 → 11

localize18.0ms

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)))

rewrite54.0ms

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×	`expm1-log1p-u` `cbrt-div` `flip3--` `flip--` `log1p-expm1-u` `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 → 164

Calls

4 calls:

36.0ms	(* (/ x (/ (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(* (/ x (/ (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
61.0ms	(sqrt (- (* z z) (* t a)))
56.0ms	(sqrt (- (* z z) (* t a)))
85.0ms	(cbrt (- (* z z) (* t a)))

simplify109.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	991	3533
1	4149	3232
2	5002	3220

prune646.0ms

Filtered

176 candidates to 144 candidates (81.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	176	11	187

Merged error: 2.9b

Counts

187 → 11

regimes590.0ms

Accuracy

80% (4.3b remaining)

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

bsearch80.0ms

Steps

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample798.0ms

Algorithm

intervals

Results

336.0ms	8863×	body	80	valid
104.0ms	2803×	body	80	nan