Details

analyze235.0ms (3.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4920	34
1	4920	34
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample44.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true
0.0ms	4×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4836	17
1	4836	17

prune4.0ms (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

15.3b

Counts

2 → 2

Compiler

Compiled 35 to 26 computations (25.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 a a) (.f64 b b))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
14.9b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite74.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

8×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
7×	`add-sqr-sqrt_binary64_1464`
6×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
5×	`add-log-exp_binary64_1481`
4×	`pow1_binary64_1503` `times-frac_binary64_1448` `associate-/l*_binary64_1387`
3×	`difference-of-squares_binary64_1411` `sqrt-prod_binary64_1458`
2×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417`
1×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `associate-/r*_binary64_1386` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

3 → 52

Calls

3 calls:

8.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
5.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 1164 to 244 computations (79% saved)

series485.0ms (7.3%)

Error

0.5b

Counts

3 → 30

Calls

3 calls:

270.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
104.0ms	(-.f64 (.f64 a a) (.f64 b b))
89.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 870 to 747 computations (14.1% saved)

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4937	1189
1	4937	1189

prune104.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Error

Counts

84 → 3

Compiler

Compiled 1297 to 416 computations (67.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 a (*.f64 b (/.f64 b a)))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
0.0b	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
0.1b	(*.f64 b (/.f64 b a))

rewrite150.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

27×	`add-sqr-sqrt_binary64_1464`
21×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
19×	`times-frac_binary64_1448`
13×	`associate-r_binary64_1382`
11×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
7×	`pow1_binary64_1503`
6×	`add-log-exp_binary64_1481`
3×	`associate-l_binary64_1383` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `sqrt-prod_binary64_1458`
2×	`div-exp_binary64_1493` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `cbrt-undiv_binary64_1476` `unswap-sqr_binary64_1410` `div-inv_binary64_1439` `flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417`
1×	`pow-prod-down_binary64_1513` `associate-r/_binary64_1384` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

4 → 87

Calls

4 calls:

14.0ms	(*.f64 b (/.f64 b a))
10.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
6.0ms	(-.f64 a (*.f64 b (/.f64 b a)))
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))

Compiler

Compiled 1711 to 491 computations (71.3% saved)

series580.0ms (8.7%)

Error

Counts

4 → 36

Calls

4 calls:

226.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
154.0ms	(-.f64 a (*.f64 b (/.f64 b a)))
84.0ms	(*.f64 b (/.f64 b a))
82.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))

Compiler

Compiled 972 to 794 computations (18.3% saved)

simplify119.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5071	1715

prune120.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	123	3	126

Error

Counts

126 → 3

Compiler

Compiled 1910 to 602 computations (68.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))
0.0b	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
0.0b	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
0.1b	(*.f64 b (/.f64 b a))

rewrite285.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

100×	`times-frac_binary64_1448`
71×	`add-sqr-sqrt_binary64_1464`
65×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
22×	`add-exp-log_binary64_1480`
18×	`associate-/r*_binary64_1386`
16×	`add-cbrt-cube_binary64_1478`
13×	`associate-r_binary64_1382`
11×	`associate-/r/_binary64_1388`
9×	`div-exp_binary64_1493`
8×	`pow1_binary64_1503`
7×	`div-inv_binary64_1439`
6×	`associate-/l*_binary64_1387`
5×	`cbrt-undiv_binary64_1476` `flip3--_binary64_1446` `flip--_binary64_1417`
4×	`add-log-exp_binary64_1481`
3×	`associate-l_binary64_1383` `sqrt-prod_binary64_1458`
2×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `1-exp_binary64_1486` `rec-exp_binary64_1492` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`pow-prod-down_binary64_1513` `associate-r/_binary64_1384` `-commutative_binary64_1373` `inv-pow_binary64_1527` `pow-flip_binary64_1516` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455`

Counts

4 → 158

Calls

4 calls:

16.0ms	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
15.0ms	(*.f64 b (/.f64 b a))
9.0ms	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))

Compiler

Compiled 3933 to 1369 computations (65.2% saved)

series497.0ms (7.5%)

Error

Counts

4 → 39

Calls

4 calls:

158.0ms	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
156.0ms	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
84.0ms	(*.f64 b (/.f64 b a))
68.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))

Compiler

Compiled 1317 to 1145 computations (13.1% saved)

simplify141.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4964	3928
1	4964	3928

prune212.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	197	3	200

Error

Counts

200 → 3

Compiler

Compiled 3897 to 1365 computations (65% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) a)
0.0b	(/.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) a)
14.7b	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
14.7b	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

rewrite345.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

42×	`times-frac_binary64_1448`
40×	`add-sqr-sqrt_binary64_1464` `sqrt-prod_binary64_1458`
38×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
14×	`associate-/l*_binary64_1387`
10×	`difference-of-squares_binary64_1411`
8×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459`
6×	`pow1_binary64_1503` `associate-/r*_binary64_1386`
4×	`add-log-exp_binary64_1481` `flip3--_binary64_1446` `flip--_binary64_1417` `associate-/l/_binary64_1389`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439`

Counts

4 → 122

Calls

4 calls:

8.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) a)
8.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) a)
5.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
5.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 4150 to 636 computations (84.7% saved)

series770.0ms (11.6%)

Error

Counts

4 → 48

Calls

4 calls:

212.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) a)
200.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) a)
150.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
148.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 3128 to 2034 computations (35% saved)

simplify124.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5539	3354

prune198.0ms (3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	170	3	173

Error

Counts

173 → 3

Compiler

Compiled 4966 to 975 computations (80.4% saved)

regimes404.0ms (6.1%)

Accuracy

Total 0.0b remaining (88.5%)

Threshold costs 0.0b (88.5%)

Compiler

Compiled 2335 to 1568 computations (32.8% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms (0%)

sample1.5s (23%)

Algorithm

1×

intervals

Results

423.0ms	8000×	body	128	valid
236.0ms	8000×	pre	128	true
3.0ms	127×	pre	128	false

Compiler

Compiled 290 to 197 computations (32.1% saved)

Details

analyze235.0ms (3.5%)

sample44.0ms (0.7%)

simplify109.0ms (1.6%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite74.0ms (1.1%)

series485.0ms (7.3%)

simplify59.0ms (0.9%)

prune104.0ms (1.6%)

localize15.0ms (0.2%)

rewrite150.0ms (2.3%)

series580.0ms (8.7%)

simplify119.0ms (1.8%)

prune120.0ms (1.8%)

localize18.0ms (0.3%)

rewrite285.0ms (4.3%)

series497.0ms (7.5%)

simplify141.0ms (2.1%)

prune212.0ms (3.2%)

localize9.0ms (0.1%)

rewrite345.0ms (5.2%)

series770.0ms (11.6%)

simplify124.0ms (1.9%)

prune198.0ms (3%)

regimes404.0ms (6.1%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.5s (23%)

Profiling