Details

analyze1.1s (25.3%)

Algorithm

1×

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

sample41.0ms (0.9%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	80	valid
3.0ms	73×	body	80	nan
2.0ms	34×	body	80	invalid

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune9.0ms (0.2%)

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 (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
5.3b	(* (* x y) z)
7.8b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.6b	(sqrt (- (* z z) (* t a)))

rewrite24.0ms (0.5%)

Algorithm

1×	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 → 75

Calls

4 calls:

9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
5.0ms	(* (* x y) z)
4.0ms	(- (* z z) (* t a))
4.0ms	(sqrt (- (* z z) (* t a)))

series59.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms	(sqrt (- (* z z) (* t a)))
7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)

simplify36.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5307	972

prune149.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	8	88

Merged error: 3.0b

Counts

88 → 8

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
3.0b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.6b	(sqrt (- (* z z) (* t a)))

rewrite28.0ms (0.6%)

Algorithm

1×	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:

11.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
6.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(- (* z z) (* t a))

series62.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
14.0ms	(sqrt (- (* z z) (* t a)))
10.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))

simplify50.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5256	1640

prune156.0ms (3.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	121	10	131

Merged error: 3.0b

Counts

131 → 10

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
0.7b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.1b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
22.6b	(sqrt (- (* z z) (* t a)))

rewrite32.0ms (0.7%)

Algorithm

1×	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:

11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(- (* z z) (* t a))

series70.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
21.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))
7.0ms	(- (* z z) (* t a))

simplify46.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune141.0ms (3.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	102	11	113

Merged error: 3.0b

Counts

113 → 11

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

14.0b	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
22.6b	(sqrt (- (* z z) (* t a)))
22.6b	(sqrt (- (* z z) (* t a)))
22.6b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms (0.5%)

Algorithm

1×	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)))

series106.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
12.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5509	786

prune90.0ms (2.1%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	67	11	78

Merged error: 3.0b

Counts

78 → 11

regimes988.0ms (22.6%)

Accuracy

Total 3.0b remaining (46.9%)

Threshold costs 0b (0%)

bsearch125.0ms (2.9%)

Steps

Iters	Range		Point
8	2.3182363157074874e+140	2.4327913402753088e+143	1.0018756625348413e+142
9	-3.0273427999488094e-280	-1.2904722683531297e-288	-2.403671892753973e-282
10	-8.421225428739286e-151	-2.432862960168308e-165	-4.636365954139031e-158
8	-5.636726367833887e+92	-7.924427136884148e+89	-5.539714192103757e+92

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	65
1	80	65

end0.0ms (0%)

sample899.0ms (20.6%)

Algorithm

1×

intervals

Results

407.0ms	8000×	body	80	valid
110.0ms	2234×	body	80	nan
44.0ms	898×	body	80	invalid

Details

analyze1.1s (25.3%)

sample41.0ms (0.9%)

simplify39.0ms (0.9%)

prune9.0ms (0.2%)

localize10.0ms (0.2%)

rewrite24.0ms (0.5%)

series59.0ms (1.3%)

simplify36.0ms (0.8%)

prune149.0ms (3.4%)

localize10.0ms (0.2%)

rewrite28.0ms (0.6%)

series62.0ms (1.4%)

simplify50.0ms (1.2%)

prune156.0ms (3.6%)

localize12.0ms (0.3%)

rewrite32.0ms (0.7%)

series70.0ms (1.6%)

simplify46.0ms (1.1%)

prune141.0ms (3.2%)

localize19.0ms (0.4%)

rewrite22.0ms (0.5%)

series106.0ms (2.4%)

simplify42.0ms (1%)

prune90.0ms (2.1%)

regimes988.0ms (22.6%)

bsearch125.0ms (2.9%)

simplify2.0ms (0%)

end0.0ms (0%)

sample899.0ms (20.6%)

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