Details

analyze2.1s (23.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 19 to 19 computations (0% saved)

sample47.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
7.0ms	102×	body	128	nan
4.0ms	53×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify129.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	6100	27

prune7.0ms (0.1%)

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

Error

14.6b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.3b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
11.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1480`
38×	`add-sqr-sqrt_binary64_1464`
27×	`prod-exp_binary64_1491`
23×	`add-cbrt-cube_binary64_1478`
19×	`associate-r_binary64_1382` `div-exp_binary64_1493`
17×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
15×	`times-frac_binary64_1448`
13×	`associate-l_binary64_1383`
10×	`pow-exp_binary64_1510` `unswap-sqr_binary64_1410`
7×	`cbrt-unprod_binary64_1475` `sqrt-prod_binary64_1458` `pow1_binary64_1503` `unpow-prod-down_binary64_1521`
5×	`cbrt-undiv_binary64_1476`
4×	`sqrt-div_binary64_1459` `add-log-exp_binary64_1481`
3×	`associate-*r/_binary64_1384` `unpow2_binary64_1507` `div-inv_binary64_1439` `sqr-pow_binary64_1414`
2×	`flip3--_binary64_1446` `*-commutative_binary64_1373` `flip--_binary64_1417` `pow-to-exp_binary64_1511`
1×	`sqrt-pow1_binary64_1460` `associate-/r_binary64_1386` `rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `associate-/l_binary64_1387` `pow-prod-down_binary64_1513` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`

Counts

4 → 116

Calls

4 calls:

12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series549.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

282.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
155.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
90.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
21.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5147	2845

prune189.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Error

7.1b

Counts

129 → 10

Compiler

Compiled 3381 to 1981 computations (41.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.3b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
4.8b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1480`
26×	`prod-exp_binary64_1491`
23×	`add-cbrt-cube_binary64_1478`
20×	`add-sqr-sqrt_binary64_1464` `div-exp_binary64_1493`
13×	`*-un-lft-identity_binary64_1442`
10×	`associate-r_binary64_1382` `pow-exp_binary64_1510` `add-cube-cbrt_binary64_1477`
6×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sqrt-prod_binary64_1458` `unpow-prod-down_binary64_1521`
5×	`times-frac_binary64_1448` `pow1_binary64_1503`
4×	`associate-/r*_binary64_1386` `add-log-exp_binary64_1481` `unswap-sqr_binary64_1410`
3×	`div-inv_binary64_1439` `associate-l_binary64_1383`
2×	`unpow2_binary64_1507` `clear-num_binary64_1441` `associate-/l*_binary64_1387` `sqrt-div_binary64_1459` `frac-2neg_binary64_1453` `sqr-pow_binary64_1414` `difference-of-squares_binary64_1411` `pow-to-exp_binary64_1511`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `flip3--_binary64_1446` `*-commutative_binary64_1373` `flip--_binary64_1417` `pow1/2_binary64_1522` `distribute-lft-out--_binary64_1394`

Counts

4 → 99

Calls

4 calls:

8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
8.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series525.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

307.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
104.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
91.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5069	2178

prune144.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Error

6.6b

Counts

121 → 10

Compiler

Compiled 2769 to 1785 computations (35.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
5.9b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
116×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
87×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
10×	`add-sqr-sqrt_binary64_1464`
8×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`times-frac_binary64_1448` `pow1_binary64_1503`
5×	`associate-r_binary64_1382` `associate-/r*_binary64_1386`
4×	`associate-*r/_binary64_1384` `div-inv_binary64_1439` `add-log-exp_binary64_1481`
3×	`associate-/l/_binary64_1389` `clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-l*_binary64_1383` `frac-2neg_binary64_1453`
1×	`pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-times_binary64_1452` `associate-l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 153

Calls

4 calls:

18.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
9.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series186.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
39.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))
21.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify103.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5025	3130

prune210.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	166	9	175

Error

6.6b

Counts

175 → 9

Compiler

Compiled 4387 to 2575 computations (41.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.2b	(/.f64 (.f64 2 d) (.f64 M D))
4.5b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 1 (/.f64 (.f64 2 d) (.f64 M D)))) l)
5.9b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite99.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

718×	`add-exp-log_binary64_1480`
329×	`prod-exp_binary64_1491`
312×	`add-cbrt-cube_binary64_1478`
305×	`div-exp_binary64_1493`
131×	`cbrt-unprod_binary64_1475`
127×	`cbrt-undiv_binary64_1476`
30×	`1-exp_binary64_1486` `rec-exp_binary64_1492`
10×	`add-sqr-sqrt_binary64_1464`
8×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`times-frac_binary64_1448` `pow1_binary64_1503`
5×	`associate-r_binary64_1382` `associate-/r*_binary64_1386`
4×	`associate-*r/_binary64_1384` `associate-/l/_binary64_1389` `div-inv_binary64_1439` `add-log-exp_binary64_1481`
3×	`clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-l*_binary64_1383` `frac-2neg_binary64_1453`
1×	`pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-times_binary64_1452` `un-div-inv_binary64_1440` `associate-l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 226

Calls

4 calls:

25.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 1 (/.f64 (.f64 2 d) (.f64 M D)))) l)
13.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
6.0ms	(/.f64 (.f64 2 d) (.f64 M D))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series194.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 1 (/.f64 (.f64 2 d) (.f64 M D)))) l)
41.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
28.0ms	(/.f64 (.f64 M D) (.f64 2 d))
21.0ms	(/.f64 (.f64 2 d) (.f64 M D))

simplify129.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4964	5269
1	4964	5269

prune255.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	238	9	247

Error

6.6b

Counts

247 → 9

Compiler

Compiled 6248 to 2908 computations (53.5% saved)

regimes1.3s (15%)

Accuracy

Total 2.2b remaining (24.6%)

Threshold costs 0b (0%)

Compiler

Compiled 18238 to 15647 computations (14.2% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	140	39
1	140	39

end0.0ms (0%)

sample2.3s (26.3%)

Algorithm

1×

intervals

Results

615.0ms	8000×	body	128	valid
230.0ms	3176×	body	128	nan
104.0ms	1346×	body	128	invalid

Compiler

Compiled 1104 to 943 computations (14.6% saved)

Details

analyze2.1s (23.7%)

sample47.0ms (0.5%)

simplify129.0ms (1.4%)

prune7.0ms (0.1%)

localize15.0ms (0.2%)

rewrite42.0ms (0.5%)

series549.0ms (6.2%)

simplify74.0ms (0.8%)

prune189.0ms (2.1%)

localize14.0ms (0.2%)

rewrite41.0ms (0.5%)

series525.0ms (5.9%)

simplify50.0ms (0.6%)

prune144.0ms (1.6%)

localize18.0ms (0.2%)

rewrite63.0ms (0.7%)

series186.0ms (2.1%)

simplify103.0ms (1.2%)

prune210.0ms (2.4%)

localize16.0ms (0.2%)

rewrite99.0ms (1.1%)

series194.0ms (2.2%)

simplify129.0ms (1.5%)

prune255.0ms (2.9%)

regimes1.3s (15%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.3s (26.3%)

Profiling