Details

sample49.0ms

Algorithm

intervals

Results

13.0ms	288×	body	80	valid
5.0ms	111×	body	80	nan

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 24.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
4.2b	(* (* x y) z)
8.7b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.5b	(sqrt (- (* z z) (* t a)))

rewrite21.0ms

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))
4.0ms	(* (* x y) z)
8.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms	(sqrt (- (* z z) (* t a)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* z z) (* t a))
28.0ms	(* (* x y) z)
83.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
74.0ms	(sqrt (- (* z z) (* t a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	343	583
1	1850	515
2	5003	510

prune275.0ms

Filtered

88 candidates to 60 candidates (31.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	7	89

Merged error: 1.7b

Counts

89 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.6b	(- (* z z) (* t a))
1.8b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
25.5b	(sqrt (- (* z z) (* t a)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
3×	`flip3--` `flip--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

6.0ms	(/ (sqrt (- (* z z) (* t a))) z)
3.0ms	(- (* z z) (* t a))
8.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
3.0ms	(sqrt (- (* z z) (* t a)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (sqrt (- (* z z) (* t a))) z)
39.0ms	(- (* z z) (* t a))
83.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
73.0ms	(sqrt (- (* z z) (* t a)))

simplify60.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	512	1325
1	2358	1230
2	5002	1214

prune670.0ms

Filtered

144 candidates to 99 candidates (31.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	143	8	151

Merged error: 1.7b

Counts

151 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
2.0b	(/ (* x y) (sqrt (- (* z z) (* t a))))
8.2b	(* (/ (* x y) (sqrt (- (* z z) (* t a)))) z)
25.5b	(sqrt (- (* z z) (* t a)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac` `associate-l` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r/` `flip--`
3×	`associate-r`
2×	`div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l*` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
7.0ms	(/ (* x y) (sqrt (- (* z z) (* t a))))
10.0ms	(* (/ (* x y) (sqrt (- (* z z) (* t a)))) z)
4.0ms	(sqrt (- (* z z) (* t a)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* z z) (* t a))
73.0ms	(/ (* x y) (sqrt (- (* z z) (* t a))))
86.0ms	(* (/ (* x y) (sqrt (- (* z z) (* t a)))) z)
79.0ms	(sqrt (- (* z z) (* t a)))

simplify47.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	361	763
1	1630	671
2	5002	665

prune371.0ms

Filtered

100 candidates to 70 candidates (30.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	100	8	108

Merged error: 1.7b

Counts

108 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ 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)))

rewrite84.0ms

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:

5.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
56.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
6.0ms	(cbrt (- (* z z) (* t a)))
6.0ms	(cbrt (- (* z z) (* t a)))

series569.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
329.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
92.0ms	(cbrt (- (* z z) (* t a)))
95.0ms	(cbrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1081	3457
1	5001	3199

prune2.1s

Filtered

221 candidates to 182 candidates (17.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	221	8	229

Merged error: 1.7b

Counts

229 → 8

regimes834.0ms

Accuracy

80.9% (4.0b remaining)

Error of 7.4b against oracle of 3.4b and baseline of 24.3b

bsearch102.0ms

Steps

Iters	Range		Point
8	4.869233091185986e+119	3.101993157480737e+123	6.636192047875887e+119
7	-8.524146073457441e+106	-2.1448952547636657e+105	-2.8021315270695464e+105

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	31	10
2	31	10

end0.0ms

sample1.2s

Algorithm

intervals

Results

443.0ms	8835×	body	80	valid
143.0ms	3015×	body	80	nan

Details

sample49.0ms

simplify9.0ms

prune5.0ms

localize10.0ms

rewrite21.0ms

series222.0ms

simplify49.0ms

prune275.0ms

localize10.0ms

rewrite25.0ms

series281.0ms

simplify60.0ms

prune670.0ms

localize11.0ms

rewrite26.0ms

series279.0ms

simplify47.0ms

prune371.0ms

localize22.0ms

rewrite84.0ms

series569.0ms

simplify51.0ms

prune2.1s

regimes834.0ms

bsearch102.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling