Details

analyze2.1s (26%)

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)

sample49.0ms (0.6%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
7.0ms	93×	body	128	nan
3.0ms	47×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify128.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	6100	27

prune3.0ms (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: 16.6b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.1b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.7b	(/.f64 (.f64 M D) (.f64 2 d))
14.7b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite45.0ms (0.6%)

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))
11.0ms	(.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))))

series556.0ms (7%)

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)))))
166.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
84.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5147	2845

prune172.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Merged error: 7.8b

Counts

129 → 9

Compiler

Compiled 3292 to 1917 computations (41.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) l))))
3.7b	(/.f64 (.f64 M D) (.f64 2 d))
5.8b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
6.9b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64_1480`
27×	`prod-exp_binary64_1491`
25×	`add-cbrt-cube_binary64_1478` `add-sqr-sqrt_binary64_1464`
20×	`div-exp_binary64_1493`
19×	`associate-r_binary64_1382`
15×	`*-un-lft-identity_binary64_1442`
12×	`add-cube-cbrt_binary64_1477`
10×	`pow-exp_binary64_1510`
7×	`cbrt-unprod_binary64_1475` `sqrt-prod_binary64_1458`
6×	`cbrt-undiv_binary64_1476` `associate-l_binary64_1383` `pow1_binary64_1503` `unpow-prod-down_binary64_1521` `unswap-sqr_binary64_1410`
5×	`times-frac_binary64_1448`
4×	`associate-/r*_binary64_1386` `add-log-exp_binary64_1481`
3×	`div-inv_binary64_1439`
2×	`associate-r/_binary64_1384` `unpow2_binary64_1507` `clear-num_binary64_1441` `associate-/l_binary64_1387` `*-commutative_binary64_1373` `sqrt-div_binary64_1459` `frac-2neg_binary64_1453` `sqr-pow_binary64_1414` `difference-of-squares_binary64_1411` `pow-to-exp_binary64_1511`
1×	`flip3--_binary64_1446` `pow-prod-down_binary64_1513` `flip--_binary64_1417` `distribute-lft-out--_binary64_1394`

Counts

4 → 108

Calls

4 calls:

11.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) l))))
10.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series641.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

420.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) l))))
106.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
93.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5284	2380

prune153.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Merged error: 6.9b

Counts

129 → 8

Compiler

Compiled 3000 to 1909 computations (36.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.7b	(/.f64 (.f64 M D) (.f64 2 d))
3.7b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
5.8b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)

rewrite63.0ms (0.8%)

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)
8.0ms	(.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))

series205.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
46.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))
21.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify101.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5025	3130

prune210.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	166	7	173

Merged error: 6.9b

Counts

173 → 7

Compiler

Compiled 4327 to 2523 computations (41.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.6b	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
3.7b	(/.f64 (.f64 M D) (.f64 2 d))
3.7b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
22×	`times-frac_binary64_1448`
21×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `div-exp_binary64_1493`
18×	`add-sqr-sqrt_binary64_1464`
16×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`div-inv_binary64_1439`
7×	`associate-/l*_binary64_1387`
6×	`pow1_binary64_1503`
5×	`associate-r_binary64_1382` `associate-/r*_binary64_1386`
4×	`add-log-exp_binary64_1481`
3×	`clear-num_binary64_1441` `associate-l_binary64_1383` `frac-2neg_binary64_1453`
1×	`associate-r/_binary64_1384` `associate-/l/_binary64_1389` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `unswap-sqr_binary64_1410`

Counts

4 → 115

Calls

4 calls:

9.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
8.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series122.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
36.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5000	1883

prune150.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Merged error: 6.9b

Counts

134 → 7

Compiler

Compiled 3568 to 1951 computations (45.3% saved)

regimes936.0ms (11.8%)

Compiler: Compiled 11678 to 10295 computations (11.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	36
1	89	36

end0.0ms (0%)

sample2.0s (25.1%)

Algorithm

1×

intervals

Results

587.0ms	8000×	body	128	valid
221.0ms	3095×	body	128	nan
93.0ms	1257×	body	128	invalid

Compiler

Compiled 764 to 668 computations (12.6% saved)

Details

analyze2.1s (26%)

sample49.0ms (0.6%)

simplify128.0ms (1.6%)

prune3.0ms (0%)

localize13.0ms (0.2%)

rewrite45.0ms (0.6%)

series556.0ms (7%)

simplify68.0ms (0.9%)

prune172.0ms (2.2%)

localize13.0ms (0.2%)

rewrite46.0ms (0.6%)

series641.0ms (8.1%)

simplify50.0ms (0.6%)

prune153.0ms (1.9%)

localize16.0ms (0.2%)

rewrite63.0ms (0.8%)

series205.0ms (2.6%)

simplify101.0ms (1.3%)

prune210.0ms (2.7%)

localize13.0ms (0.2%)

rewrite43.0ms (0.5%)

series122.0ms (1.5%)

simplify74.0ms (0.9%)

prune150.0ms (1.9%)

regimes936.0ms (11.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (25.1%)

Profiling