Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample35.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
2.0ms	55×	body	80	nan
1.0ms	25×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	77	14
1	77	14

prune14.0ms

Filtered

1 candidates to 1 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: 22.6b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.0b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.2b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.7b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
3.0ms	(sqrt (- (* z z) (* t a)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
19.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
35.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4979	1238
1	4979	1238

prune147.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	94	11	105

Merged error: 3.0b

Counts

105 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
2.4b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.7b	(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
3.0ms	(- (* z z) (* t a))
11.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms	(sqrt (- (* z z) (* t a)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
34.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5165	1640

prune153.0ms

Filtered

83 candidates to 123 candidates (-48.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	5	4	9
Picked	1	0	1
Done	0	1	1
Total	122	12	134

Merged error: 3.0b

Counts

134 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
0.8b	(- (* z z) (* t a))
2.4b	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
25.7b	(sqrt (- (* z z) (* t a)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
143×	`add-sqr-sqrt`
142×	`add-cube-cbrt` `*-un-lft-identity`
71×	`associate-r`
66×	`sqrt-prod`
60×	`add-exp-log`
30×	`add-cbrt-cube`
22×	`associate-/r*`
21×	`div-exp` `prod-exp`
11×	`pow1`
9×	`cbrt-undiv` `cbrt-unprod` `div-inv`
6×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow-prod-down` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 242

Calls

4 calls:

9.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
3.0ms	(- (* z z) (* t a))
19.0ms	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
7.0ms	(- (* z z) (* t a))
36.0ms	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify73.0ms

Algorithm

egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4959	4096
1	4959	4096

prune216.0ms

Filtered

140 candidates to 254 candidates (-81.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	252	2	254
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	256	10	266

Merged error: 3.0b

Counts

266 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
2.4b	(* (* x y) (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
26.5b	(cbrt (- (* z z) (* t a)))
26.5b	(cbrt (- (* z z) (* t a)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
11×	`prod-exp` `cbrt-unprod`
9×	`pow1` `associate-r`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `cbrt-div` `add-log-exp`
4×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
3×	`times-frac` `associate-*r/` `pow-prod-down`
2×	`pow1/3` `sqrt-div` `associate-/r/`
1×	`sub-neg` `diff-log` `associate-l` `*-commutative` `div-inv`

Counts

4 → 70

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
11.0ms	(* (* x y) (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
3.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
89.0ms	(* (* x y) (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
24.0ms	(cbrt (- (* z z) (* t a)))
26.0ms	(cbrt (- (* z z) (* t a)))

simplify26.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5276	1429

prune99.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	82	10	92

Merged error: 3.0b

Counts

92 → 10

regimes931.0ms

Accuracy

83% (3.4b remaining)

Error of 6.6b against oracle of 3.2b and baseline of 23.0b

bsearch2.6s

Steps

Iters	Range		Point
7	3.842945134529307e+102	6.300925754254255e+104	5.4385652297170126e+104
8	-1.7980666331071503e+158	-2.9521560266194137e+153	-1.2327965780524498e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	31
1	31	31

end0.0ms

analyze1.3s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample899.0ms

Algorithm

intervals

Results

411.0ms	8000×	body	80	valid
109.0ms	2270×	body	80	nan
45.0ms	861×	body	80	invalid

Details

analyze1.1s

sample35.0ms

simplify3.0ms

prune14.0ms

localize10.0ms

rewrite31.0ms

series75.0ms

simplify54.0ms

prune147.0ms

localize11.0ms

rewrite27.0ms

series66.0ms

simplify61.0ms

prune153.0ms

localize12.0ms

rewrite49.0ms

series68.0ms

simplify73.0ms

prune216.0ms

localize14.0ms

rewrite24.0ms

series145.0ms

simplify26.0ms

prune99.0ms

regimes931.0ms

bsearch2.6s

simplify1.0ms

end0.0ms

analyze1.3s

sample899.0ms

Profiling