Details

sample40.0ms

Algorithm

intervals

Results

14.0ms	286×	body	80	valid
4.0ms	77×	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

prune7.0ms

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: 24.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* z z) (* t a))
5.2b	(* (* x y) z)
10.8b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

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

series54.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
28.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

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

prune125.0ms

Filtered

88 candidates to 60 candidates (31.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 1.9b

Counts

89 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (- (* z z) (* t a))) z)
1.2b	(- (* z z) (* t a))
3.3b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite26.0ms

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))
9.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
3.0ms	(sqrt (- (* z z) (* t a)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (sqrt (- (* z z) (* t a))) z)
7.0ms	(- (* z z) (* t a))
28.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (49.0ms)

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

prune141.0ms

Filtered

144 candidates to 99 candidates (31.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	143	9	152

Merged error: 1.9b

Counts

152 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.2b	(- (* z z) (* t a))
3.4b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 227

Calls

4 calls:

21.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
3.0ms	(- (* z z) (* t a))
9.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
7.0ms	(- (* z z) (* t a))
17.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify108.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	814	2501
1	3992	2347
2	5002	2347

prune187.0ms

Filtered

239 candidates to 159 candidates (33.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	237	2	239
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	239	9	248

Merged error: 1.9b

Counts

248 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(* x (/ (* y (* (cbrt z) (cbrt z))) (/ (sqrt (- (* z z) (* t a))) (cbrt z))))
1.2b	(- (* z z) (* t a))
6.5b	(/ (* y (* (cbrt z) (cbrt z))) (/ (sqrt (- (* z z) (* t a))) (cbrt z)))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

188×	`times-frac`
85×	`add-sqr-sqrt`
82×	`add-cube-cbrt` `*-un-lft-identity`
57×	`sqrt-prod`
54×	`add-exp-log` `cbrt-prod`
45×	`associate-r`
40×	`associate-/r*` `add-cbrt-cube`
19×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
7×	`pow1`
6×	`add-log-exp`
5×	`div-inv`
3×	`associate-l`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l*` `unswap-sqr`

Counts

4 → 204

Calls

4 calls:

25.0ms	(* x (/ (* y (* (cbrt z) (cbrt z))) (/ (sqrt (- (* z z) (* t a))) (cbrt z))))
3.0ms	(- (* z z) (* t a))
15.0ms	(/ (* y (* (cbrt z) (cbrt z))) (/ (sqrt (- (* z z) (* t a))) (cbrt z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* x (/ (* y (* (cbrt z) (cbrt z))) (/ (sqrt (- (* z z) (* t a))) (cbrt z))))
7.0ms	(- (* z z) (* t a))
21.0ms	(/ (* y (* (cbrt z) (cbrt z))) (/ (sqrt (- (* z z) (* t a))) (cbrt z)))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify118.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	900	2818
1	4632	2548
2	5002	2445

prune145.0ms

Filtered

216 candidates to 137 candidates (36.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	216	9	225

Merged error: 1.9b

Counts

225 → 9

regimes755.0ms

Accuracy

80.4% (3.9b remaining)

Error of 6.8b against oracle of 3.0b and baseline of 22.7b

bsearch71.0ms

Steps

Iters	Range		Point
10	5165044110.2207775	1.7307442407338173e+23	1.3390747651094517e+23
10	-1.5324879470505324e+57	-2.5336327888462263e+41	-7.898382149597823e+54

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	15
1	36	15
2	36	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

446.0ms	8894×	body	80	valid
141.0ms	2953×	body	80	nan

Details

sample40.0ms

simplify9.0ms

prune7.0ms

localize10.0ms

rewrite22.0ms

series54.0ms

simplify50.0ms

prune125.0ms

localize10.0ms

rewrite26.0ms

series61.0ms

simplify62.0ms

prune141.0ms

localize10.0ms

rewrite51.0ms

series65.0ms

simplify108.0ms

prune187.0ms

localize14.0ms

rewrite59.0ms

series76.0ms

simplify118.0ms

prune145.0ms

regimes755.0ms

bsearch71.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling