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

sample40.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	77×	body	80	nan
1.0ms	28×	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

prune13.0ms

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: 23.4b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.0b	(* y (/ z (sqrt (- (* z z) (* t a)))))
24.4b	(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))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
29.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
18.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
16.0ms	(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4979	1238
1	4979	1238

prune172.0ms

Filtered

74 candidates to 103 candidates (-39.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	91	12	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	92	13	105

Merged error: 3.8b

Counts

105 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

1.6b	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
24.4b	(sqrt (- (* z z) (* t a)))
24.4b	(sqrt (- (* z z) (* t a)))
24.4b	(sqrt (- (* z z) (* t a)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
37×	`prod-exp` `add-cbrt-cube` `cbrt-unprod`
21×	`pow1`
11×	`add-sqr-sqrt`
10×	`pow-prod-down`
9×	`cbrt-undiv` `div-exp` `sqrt-prod`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `flip--`
1×	`frac-times` `associate-r` `associate-l/` `-commutative`

Counts

4 → 86

Calls

4 calls:

30.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (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)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
13.0ms	(sqrt (- (* z z) (* t a)))
17.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4936	1175
1	4936	1175

prune129.0ms

Filtered

62 candidates to 98 candidates (-58.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	98	13	111

Merged error: 3.8b

Counts

111 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b	(* x (* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))))
2.0b	(* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
25.3b	(cbrt (- (* z z) (* t a)))
25.3b	(cbrt (- (* z z) (* t a)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`cbrt-prod` `cbrt-div` `associate-l`
5×	`associate-*r/`
4×	`cbrt-undiv` `div-exp` `pow-prod-down` `add-log-exp`
3×	`flip3--` `times-frac` `flip--`
2×	`pow1/3` `sqrt-div` `associate-/r/` `*-commutative`
1×	`div-inv` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

11.0ms	(* x (* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))))
11.0ms	(* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
3.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* x (* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))))
58.0ms	(* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
26.0ms	(cbrt (- (* z z) (* t a)))
23.0ms	(cbrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4964	1726
1	4964	1726

prune148.0ms

Filtered

72 candidates to 90 candidates (-25.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	91	12	103

Merged error: 3.8b

Counts

103 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.0b	(* (/ z (sqrt (- (* z z) (* t a)))) x)
2.4b	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
24.4b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`associate-l`
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×	`add-log-exp`
4×	`sqrt-div` `associate-r` `pow-prod-down`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-/r/` `-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `div-inv`

Counts

4 → 91

Calls

4 calls:

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

series70.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
18.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) x)
31.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify47.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5200	1270

prune109.0ms

Filtered

74 candidates to 103 candidates (-39.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	105	10	115

Merged error: 3.8b

Counts

115 → 10

regimes1.0s

Accuracy

86.6% (2.5b remaining)

Error of 5.9b against oracle of 3.3b and baseline of 22.2b

bsearch1.3s

Steps

Iters	Range		Point
7	3.9356285225236366e+96	1.264888429882807e+98	7.70148341111315e+97
0	-5.762835744894194e+119	-5.611340619824667e+119	-5.6870881823594304e+119

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	80
1	47	80

end0.0ms

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

sample969.0ms

Algorithm

intervals

Results

428.0ms	8000×	body	80	valid
114.0ms	2243×	body	80	nan
43.0ms	855×	body	80	invalid

Details

analyze1.1s

sample40.0ms

simplify3.0ms

prune13.0ms

localize10.0ms

rewrite31.0ms

series70.0ms

simplify55.0ms

prune172.0ms

localize22.0ms

rewrite46.0ms

series78.0ms

simplify56.0ms

prune129.0ms

localize16.0ms

rewrite32.0ms

series194.0ms

simplify58.0ms

prune148.0ms

localize13.0ms

rewrite31.0ms

series70.0ms

simplify47.0ms

prune109.0ms

regimes1.0s

bsearch1.3s

simplify2.0ms

end0.0ms

analyze1.1s

sample969.0ms

Profiling