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

sample38.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
4.0ms	82×	body	80	nan
1.0ms	22×	body	80	invalid

simplify33.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	805	14
1	805	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: 21.1b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* y (/ z (sqrt (- (* z z) (* t a)))))
0.8b	(- (* z z) (* t a))
2.4b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite33.0ms

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:

12.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(- (* z z) (* t a))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* y (/ 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)))

simplify45.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune150.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Merged error: 2.5b

Counts

105 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

24.5b	(sqrt (* (* (cbrt (- (* z z) (* t a))) (cbrt (- (* z z) (* t a)))) (cbrt (- (* z z) (* t a)))))
25.4b	(cbrt (- (* z z) (* t a)))
25.4b	(cbrt (- (* z z) (* t a)))
25.4b	(cbrt (- (* z z) (* t a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

17.0ms	(sqrt (* (* (cbrt (- (* z z) (* t a))) (cbrt (- (* z z) (* t a)))) (cbrt (- (* z z) (* t a)))))
4.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (* (* (cbrt (- (* z z) (* t a))) (cbrt (- (* z z) (* t a)))) (cbrt (- (* z z) (* t a)))))
23.0ms	(cbrt (- (* z z) (* t a)))
23.0ms	(cbrt (- (* z z) (* t a)))
23.0ms	(cbrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4898	2055
1	4898	2055

prune144.0ms

Filtered

62 candidates to 101 candidates (-62.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	101	11	112

Merged error: 2.5b

Counts

112 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

8.2b	(cbrt (* y (/ z (sqrt (- (* z z) (* t a))))))
24.5b	(sqrt (- (* z z) (* t a)))
24.5b	(sqrt (- (* z z) (* t a)))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*r/`

Counts

4 → 55

Calls

4 calls:

7.0ms	(cbrt (* y (/ z (sqrt (- (* z z) (* t a))))))
6.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(cbrt (* y (/ z (sqrt (- (* z z) (* t a))))))
13.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify40.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5421	755

prune116.0ms

Filtered

57 candidates to 67 candidates (-17.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	67	11	78

Merged error: 2.5b

Counts

78 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

11.4b	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
24.5b	(sqrt (- (* z z) (* t a)))
24.5b	(sqrt (- (* z z) (* t a)))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`associate-*r/`
1×	`cbrt-prod` `cbrt-div` `pow1/3`

Counts

4 → 55

Calls

4 calls:

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

series111.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
14.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify45.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5509	786

prune82.0ms

Filtered

57 candidates to 67 candidates (-17.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	67	11	78

Merged error: 2.5b

Counts

78 → 11

regimes1.0s

Accuracy

82.6% (3.5b remaining)

Error of 6.6b against oracle of 3.1b and baseline of 23.1b

bsearch37.0ms

Steps

Iters	Range		Point
5	927174567.7239721	3177226076.593259	2883203021.7731514
7	-7.449547838155633e+148	-1.3492254336720567e+147	-9.908813752619088e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	60
1	88	60

end0.0ms

sample902.0ms

Algorithm

intervals

Results

408.0ms	8000×	body	80	valid
98.0ms	2123×	body	80	nan
46.0ms	819×	body	80	invalid

Details

analyze1.1s

sample38.0ms

simplify33.0ms

prune14.0ms

localize11.0ms

rewrite33.0ms

series73.0ms

simplify45.0ms

prune150.0ms

localize14.0ms

rewrite35.0ms

series83.0ms

simplify63.0ms

prune144.0ms

localize15.0ms

rewrite22.0ms

series86.0ms

simplify40.0ms

prune116.0ms

localize16.0ms

rewrite22.0ms

series111.0ms

simplify45.0ms

prune82.0ms

regimes1.0s

bsearch37.0ms

simplify2.0ms

end0.0ms

sample902.0ms

Profiling