Details

analyze1.1s (23.5%)

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

sample36.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	80	valid
4.0ms	81×	body	80	nan
2.0ms	37×	body	80	invalid

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune15.0ms (0.3%)

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: 22.0b

Counts

2 → 2

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
0.8b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.2b	(- (* z z) (* t a))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite37.0ms (0.8%)

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:

12.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
8.0ms	(- (* z z) (* t a))
4.0ms	(sqrt (- (* z z) (* t a)))

series69.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
18.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))
7.0ms	(- (* z z) (* t a))

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune174.0ms (3.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 2.3b

Counts

105 → 8

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(- (* z z) (* t a))
1.7b	(* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
24.6b	(sqrt (- (* z z) (* t a)))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite51.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`associate-r` `sqrt-prod`
54×	`times-frac`
45×	`add-sqr-sqrt`
43×	`add-cube-cbrt` `*-un-lft-identity`
36×	`add-exp-log`
27×	`cbrt-prod`
26×	`add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
15×	`pow1`
8×	`sqrt-div`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `add-log-exp`
5×	`associate-*r/`
4×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`frac-times` `sub-neg` `diff-log` `associate-l` `associate-l/` `-commutative` `div-inv`

Counts

4 → 132

Calls

4 calls:

33.0ms	(* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(- (* z z) (* t a))

series53.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
12.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))
7.0ms	(- (* z z) (* t a))

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4981	2892
1	4981	2892

prune215.0ms (4.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	144	8	152

Merged error: 2.3b

Counts

152 → 8

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(* (/ z (sqrt (- (* z z) (* t a)))) x)
1.2b	(- (* z z) (* t a))
1.2b	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite35.0ms (0.7%)

Algorithm

1×	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:

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

series67.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
20.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) x)
12.0ms	(sqrt (- (* z z) (* t a)))
7.0ms	(- (* z z) (* t a))

simplify36.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5505	1270

prune165.0ms (3.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	103	8	111

Merged error: 2.3b

Counts

111 → 8

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b	(- (* z z) (* t a))
7.3b	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
25.4b	(cbrt (- (* z z) (* t a)))
25.4b	(cbrt (- (* z z) (* t a)))

rewrite36.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
46×	`times-frac`
33×	`associate-r`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`sqrt-prod`
17×	`cbrt-prod`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-l`
8×	`unswap-sqr`
6×	`pow1` `cbrt-div` `add-log-exp`
4×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod`
2×	`pow1/3` `sqrt-div` `associate-/r/` `div-inv`
1×	`frac-times` `sub-neg` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 111

Calls

4 calls:

20.0ms	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
4.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(- (* z z) (* t a))
4.0ms	(cbrt (- (* z z) (* t a)))

series113.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
26.0ms	(cbrt (- (* z z) (* t a)))
22.0ms	(cbrt (- (* z z) (* t a)))
7.0ms	(- (* z z) (* t a))

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5011	2583

prune155.0ms (3.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	123	8	131

Merged error: 2.3b

Counts

131 → 8

regimes1.2s (24.3%)

Accuracy

Total 3.2b remaining (50.3%)

Threshold costs 0b (0%)

bsearch60.0ms (1.3%)

Steps

Iters	Range		Point
10	6.048374263253517e+105	3.5851473699660576e+118	1.860229807699452e+118
10	-5.41149882544799e+82	-8.807253302404127e+66	-5.342208561463816e+77

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	70
1	85	70

end0.0ms (0%)

sample897.0ms (18.9%)

Algorithm

1×

intervals

Results

403.0ms	8000×	body	80	valid
104.0ms	2326×	body	80	nan
52.0ms	898×	body	80	invalid

Details

analyze1.1s (23.5%)

sample36.0ms (0.7%)

simplify31.0ms (0.6%)

prune15.0ms (0.3%)

localize10.0ms (0.2%)

rewrite37.0ms (0.8%)

series69.0ms (1.4%)

simplify46.0ms (1%)

prune174.0ms (3.6%)

localize16.0ms (0.3%)

rewrite51.0ms (1.1%)

series53.0ms (1.1%)

simplify76.0ms (1.6%)

prune215.0ms (4.5%)

localize12.0ms (0.3%)

rewrite35.0ms (0.7%)

series67.0ms (1.4%)

simplify36.0ms (0.8%)

prune165.0ms (3.5%)

localize17.0ms (0.4%)

rewrite36.0ms (0.8%)

series113.0ms (2.4%)

simplify62.0ms (1.3%)

prune155.0ms (3.3%)

regimes1.2s (24.3%)

bsearch60.0ms (1.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample897.0ms (18.9%)

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