Details

analyze2.1s (23.3%)

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)

sample51.0ms (0.6%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
7.0ms	97×	body	128	nan
3.0ms	45×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify131.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

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: 15.9b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize17.0ms (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)))))
3.8b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
12.7b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite41.0ms (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))))

series565.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

284.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
156.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
95.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
31.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5147	2845

prune188.0ms (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

Merged error: 7.5b

Counts

129 → 10

Compiler

Compiled 3337 to 1947 computations (41.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.8b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.2b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
5.8b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

rewrite37.0ms (0.4%)

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))
7.0ms	(/.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))

series553.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

324.0ms	(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)
100.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5069	2178

prune139.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	110	11	121

Merged error: 7.3b

Counts

121 → 11

Compiler

Compiled 2777 to 1782 computations (35.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.2b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
5.5b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite68.0ms (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:

19.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
10.0ms	(/.f64 (.f64 M D) (.f64 2 d))
9.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series193.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
42.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
28.0ms	(/.f64 (.f64 M D) (.f64 2 d))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5025	3130

prune216.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	165	11	176

Merged error: 7.3b

Counts

176 → 11

Compiler

Compiled 4407 to 2590 computations (41.2% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.2b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (*.f64 (/.f64 M 2) (/.f64 D d))) l)
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
5.5b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
6.4b	(*.f64 (/.f64 M 2) (/.f64 D d))

rewrite78.0ms (0.9%)

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`
36×	`add-sqr-sqrt_binary64_1464`
27×	`times-frac_binary64_1448`
22×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
18×	`associate-r_binary64_1382`
16×	`associate-l_binary64_1383`
11×	`associate-*r/_binary64_1384`
8×	`pow1_binary64_1503`
7×	`associate-/l/_binary64_1389`
6×	`frac-times_binary64_1452`
5×	`div-inv_binary64_1439` `unswap-sqr_binary64_1410`
4×	`associate-/r_binary64_1386` `add-log-exp_binary64_1481` `associate-l/_binary64_1385`
2×	`clear-num_binary64_1441` `associate-/l_binary64_1387` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453`

Counts

4 → 186

Calls

4 calls:

24.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (*.f64 (/.f64 M 2) (/.f64 D d))) l)
12.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
9.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series194.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (*.f64 (/.f64 M 2) (/.f64 D d))) l)
42.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))
23.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

simplify134.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4964	3593
1	4964	3593

prune274.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	201	8	209

Merged error: 7.1b

Counts

209 → 8

Compiler

Compiled 5214 to 2960 computations (43.2% saved)

regimes1.3s (14.8%)

Compiler: Compiled 16596 to 14527 computations (12.5% saved)

bsearch11.0ms (0.1%)

Steps

Iters	Range		Point
2	7.131384268393432e-205	7.933606337918047e-205	7.231662027084009e-205

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	159	78
1	159	78

end0.0ms (0%)

sample2.3s (26%)

Algorithm

1×

intervals

Results

591.0ms	8000×	body	128	valid
229.0ms	3120×	body	128	nan
106.0ms	1373×	body	128	invalid

Compiler

Compiled 1091 to 941 computations (13.7% saved)

Details

analyze2.1s (23.3%)

sample51.0ms (0.6%)

simplify131.0ms (1.5%)

prune3.0ms (0%)

localize17.0ms (0.2%)

rewrite41.0ms (0.5%)

series565.0ms (6.4%)

simplify71.0ms (0.8%)

prune188.0ms (2.1%)

localize14.0ms (0.2%)

rewrite37.0ms (0.4%)

series553.0ms (6.3%)

simplify48.0ms (0.5%)

prune139.0ms (1.6%)

localize14.0ms (0.2%)

rewrite68.0ms (0.8%)

series193.0ms (2.2%)

simplify102.0ms (1.2%)

prune216.0ms (2.5%)

localize18.0ms (0.2%)

rewrite78.0ms (0.9%)

series194.0ms (2.2%)

simplify134.0ms (1.5%)

prune274.0ms (3.1%)

regimes1.3s (14.8%)

bsearch11.0ms (0.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.3s (26%)

Profiling