Details

analyze2.0s (22.1%)

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 (0.5%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
6.0ms	82×	body	128	nan
3.0ms	45×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify131.0ms (1.4%)

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: 16.0b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.9b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
12.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite41.0ms (0.4%)

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))))

series547.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

279.0ms	(.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))))
85.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
27.0ms	(/.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

prune180.0ms (1.9%)

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: 7.9b

Counts

129 → 9

Compiler

Compiled 3347 to 1952 computations (41.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.7b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
4.9b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
5.2b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`add-exp-log_binary64_1480`
91×	`prod-exp_binary64_1491`
40×	`div-exp_binary64_1493`
30×	`add-cbrt-cube_binary64_1478`
25×	`pow-exp_binary64_1510`
23×	`associate-r_binary64_1382`
22×	`add-sqr-sqrt_binary64_1464`
15×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
11×	`cbrt-unprod_binary64_1475` `times-frac_binary64_1448`
8×	`1-exp_binary64_1486` `rec-exp_binary64_1492`
7×	`pow1_binary64_1503`
6×	`cbrt-undiv_binary64_1476` `unpow-prod-down_binary64_1521`
5×	`pow-to-exp_binary64_1511`
4×	`associate-l_binary64_1383` `add-log-exp_binary64_1481` `unswap-sqr_binary64_1410`
3×	`div-inv_binary64_1439` `sqrt-prod_binary64_1458`
2×	`unpow2_binary64_1507` `*-commutative_binary64_1373` `sqrt-div_binary64_1459` `sqr-pow_binary64_1414`
1×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `associate-/r_binary64_1386` `rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `associate-/l*_binary64_1387` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `flip--_binary64_1417` `frac-2neg_binary64_1453` `un-div-inv_binary64_1440` `pow1/2_binary64_1522`

Counts

4 → 130

Calls

4 calls:

12.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))

series524.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

310.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
99.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
88.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
27.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5628	2765

prune192.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	140	11	151

Merged error: 7.4b

Counts

151 → 11

Compiler

Compiled 3603 to 2386 computations (33.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.2b	(.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
5.3b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite103.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

897×	`add-exp-log_binary64_1480`
537×	`prod-exp_binary64_1491`
487×	`add-cbrt-cube_binary64_1478`
277×	`cbrt-unprod_binary64_1475`
250×	`div-exp_binary64_1493`
131×	`cbrt-undiv_binary64_1476`
31×	`1-exp_binary64_1486` `rec-exp_binary64_1492`
16×	`associate-r_binary64_1382`
15×	`add-sqr-sqrt_binary64_1464` `pow1_binary64_1503`
13×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
12×	`times-frac_binary64_1448`
10×	`associate-*l/_binary64_1385`
7×	`pow-prod-down_binary64_1513`
6×	`associate-l_binary64_1383`
5×	`frac-times_binary64_1452`
4×	`div-inv_binary64_1439` `add-log-exp_binary64_1481`
3×	`associate-*r/_binary64_1384`
2×	`associate-/r_binary64_1386` `clear-num_binary64_1441` `associate-/l_binary64_1387` `*-commutative_binary64_1373` `frac-2neg_binary64_1453`
1×	`un-div-inv_binary64_1440` `unswap-sqr_binary64_1410`

Counts

4 → 290

Calls

4 calls:

28.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
8.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series181.0ms (2%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
45.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
30.0ms	(/.f64 (.f64 M D) (.f64 2 d))
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify149.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4978	6589
1	4978	6589

prune433.0ms (4.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	301	1	302
Fresh	1	8	9
Picked	0	1	1
Done	1	0	1
Total	303	10	313

Merged error: 7.4b

Counts

313 → 10

Compiler

Compiled 7713 to 4626 computations (40% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.9b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 (.f64 M D) h) (.f64 2 d)) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))))
5.2b	(.f64 (.f64 M D) h)
5.2b	(.f64 (.f64 (/.f64 (.f64 (.f64 M D) h) (.f64 2 d)) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite114.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

1009×	`add-exp-log_binary64_1480`
583×	`prod-exp_binary64_1491`
533×	`add-cbrt-cube_binary64_1478`
308×	`div-exp_binary64_1493`
295×	`cbrt-unprod_binary64_1475`
156×	`cbrt-undiv_binary64_1476`
36×	`1-exp_binary64_1486` `rec-exp_binary64_1492`
16×	`associate-r_binary64_1382`
15×	`pow1_binary64_1503`
14×	`add-sqr-sqrt_binary64_1464`
13×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
10×	`times-frac_binary64_1448`
6×	`pow-prod-down_binary64_1513`
5×	`frac-times_binary64_1452` `associate-*l/_binary64_1385`
4×	`add-log-exp_binary64_1481`
3×	`associate-*r/_binary64_1384` `sqrt-prod_binary64_1458`
2×	`div-inv_binary64_1439` `associate-l_binary64_1383` `*-commutative_binary64_1373` `sqrt-div_binary64_1459`
1×	`sqrt-pow1_binary64_1460` `associate-/r_binary64_1386` `rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `associate-/l_binary64_1387` `flip3--_binary64_1446` `flip--_binary64_1417` `frac-2neg_binary64_1453` `un-div-inv_binary64_1440` `pow1/2_binary64_1522`

Counts

4 → 302

Calls

4 calls:

26.0ms	(.f64 (.f64 (/.f64 (.f64 (.f64 M D) h) (.f64 2 d)) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
8.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 (.f64 M D) h) (.f64 2 d)) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(.f64 (.f64 M D) h)

series282.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

142.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 (.f64 M D) h) (.f64 2 d)) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))))
92.0ms	(.f64 (.f64 (/.f64 (.f64 (.f64 M D) h) (.f64 2 d)) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
24.0ms	(.f64 (.f64 M D) h)
24.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify133.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4979	7852
1	4979	7852

prune361.0ms (3.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	314	0	314
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	314	10	324

Merged error: 7.4b

Counts

324 → 10

Compiler

Compiled 8084 to 3640 computations (55% saved)

regimes1.3s (14.1%)

Compiler: Compiled 16194 to 14123 computations (12.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	198	85
1	198	85

end0.0ms (0%)

sample2.2s (24%)

Algorithm

1×

intervals

Results

586.0ms	8000×	body	128	valid
219.0ms	3093×	body	128	nan
98.0ms	1350×	body	128	invalid

Compiler

Compiled 1068 to 918 computations (14% saved)

Details

analyze2.0s (22.1%)

sample49.0ms (0.5%)

simplify131.0ms (1.4%)

prune3.0ms (0%)

localize17.0ms (0.2%)

rewrite41.0ms (0.4%)

series547.0ms (5.9%)

simplify74.0ms (0.8%)

prune180.0ms (1.9%)

localize14.0ms (0.2%)

rewrite46.0ms (0.5%)

series524.0ms (5.7%)

simplify57.0ms (0.6%)

prune192.0ms (2.1%)

localize14.0ms (0.2%)

rewrite103.0ms (1.1%)

series181.0ms (2%)

simplify149.0ms (1.6%)

prune433.0ms (4.7%)

localize18.0ms (0.2%)

rewrite114.0ms (1.2%)

series282.0ms (3.1%)

simplify133.0ms (1.4%)

prune361.0ms (3.9%)

regimes1.3s (14.1%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.2s (24%)

Profiling