Details

analyze433.0ms (8.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	68.6%	18.9%	6
18.7%	62.4%	18.9%	7
18.7%	59.3%	22%	8
28.1%	39%	32.9%	9
32.8%	34.3%	32.9%	10
32.8%	32%	35.3%	11
38.2%	20.7%	41.1%	12
41%	17.9%	41.1%	13
41%	16.6%	42.5%	14

sample65.0ms (1.2%)

Algorithm

1×

intervals

Results

28.0ms	116×	body	320	valid
22.0ms	133×	body	160	valid
3.0ms	43×	body	80	nan
1.0ms	7×	body	80	valid

simplify127.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4881	36
1	4881	36

prune12.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 35.0b

Counts

2 → 1

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
28.1b	(sqrt (- (* g g) (* h h)))
28.1b	(sqrt (- (* g g) (* h h)))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `flip--`
4×	`add-exp-log` `frac-times` `sqrt-div` `associate-*r/` `add-cbrt-cube` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `associate-*l/` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
11.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series139.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
61.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
7.0ms	(sqrt (- (* g g) (* h h)))
6.0ms	(sqrt (- (* g g) (* h h)))

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4978	1064
1	4978	1064

prune261.0ms (5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	55	17	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	17	73

Merged error: 29.4b

Counts

73 → 17

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
28.1b	(sqrt (- (* g g) (* h h)))
28.1b	(sqrt (- (* g g) (* h h)))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 58

Calls

4 calls:

11.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(- (* g g) (* h h))

series80.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
8.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(- (* g g) (* h h))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5184	830

prune240.0ms (4.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	70	17	87

Merged error: 28.8b

Counts

87 → 17

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
28.1b	(sqrt (- (* g g) (* h h)))
28.1b	(sqrt (- (* g g) (* h h)))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 58

Calls

4 calls:

11.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(- (* g g) (* h h))

series81.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(- (* g g) (* h h))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5184	830

prune228.0ms (4.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	16	16
Picked	1	0	1
Done	0	0	0
Total	70	17	87

Merged error: 28.8b

Counts

87 → 17

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
28.1b	(sqrt (- (* g g) (* h h)))
28.1b	(sqrt (- (* g g) (* h h)))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 58

Calls

4 calls:

12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
6.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(- (* g g) (* h h))

series274.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

255.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))
6.0ms	(- (* g g) (* h h))

simplify38.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5217	847

prune163.0ms (3.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	69	18	87

Merged error: 28.8b

Counts

87 → 18

regimes768.0ms (14.6%)

Accuracy

Total 1.3b remaining (4%)

Threshold costs 0b (0%)

bsearch45.0ms (0.9%)

Steps

Iters	Range		Point
5	-1.1746789576965113e-189	-4.911816270455327e-190	-1.1576464449940226e-189

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	129	82
1	129	82

end0.0ms (0%)

sample1.9s (37%)

Algorithm

1×

intervals

Results

924.0ms	3722×	body	320	valid
683.0ms	4113×	body	160	valid
102.0ms	1273×	body	80	nan
14.0ms	165×	body	80	valid

Details

analyze433.0ms (8.2%)

sample65.0ms (1.2%)

simplify127.0ms (2.4%)

prune12.0ms (0.2%)

localize18.0ms (0.3%)

rewrite33.0ms (0.6%)

series139.0ms (2.7%)

simplify43.0ms (0.8%)

prune261.0ms (5%)

localize20.0ms (0.4%)

rewrite24.0ms (0.5%)

series80.0ms (1.5%)

simplify62.0ms (1.2%)

prune240.0ms (4.6%)

localize19.0ms (0.4%)

rewrite23.0ms (0.4%)

series81.0ms (1.5%)

simplify62.0ms (1.2%)

prune228.0ms (4.3%)

localize20.0ms (0.4%)

rewrite28.0ms (0.5%)

series274.0ms (5.2%)

simplify38.0ms (0.7%)

prune163.0ms (3.1%)

regimes768.0ms (14.6%)

bsearch45.0ms (0.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (37%)

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