Details

analyze342.0ms (4.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2024	42
1	2024	42
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

Compiler

Compiled 21 to 20 computations (4.8% saved)

sample25.0ms (0.3%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

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

0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

rewrite188.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`add-sqr-sqrt_binary64_1464`
23×	`*-un-lft-identity_binary64_1442`
17×	`add-cube-cbrt_binary64_1477`
12×	`times-frac_binary64_1448`
11×	`pow1_binary64_1503`
10×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `associate-l_binary64_1383`
8×	`associate-*l/_binary64_1385`
7×	`associate-r_binary64_1382`
6×	`flip3--_binary64_1446` `flip--_binary64_1417`
5×	`sqrt-prod_binary64_1458`
4×	`add-log-exp_binary64_1481` `sqrt-div_binary64_1459` `associate-/r*_binary64_1386` `frac-times_binary64_1452`
3×	`associate-/l*_binary64_1387` `pow-prod-down_binary64_1513` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-/r/_binary64_1388` `sqrt-pow1_binary64_1460` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `associate-r/_binary64_1384` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `-commutative_binary64_1373`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `pow1/2_binary64_1522` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `distribute-lft-out_binary64_1393`

Counts

4 → 99

Calls

4 calls:

14.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(*.f64 (-.f64 a 1/3) 9)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 2373 to 1883 computations (20.6% saved)

series304.0ms (4.1%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

141.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
99.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
27.0ms	(*.f64 (-.f64 a 1/3) 9)
16.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 850 to 737 computations (13.3% saved)

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5010	2067

prune162.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	6	125

Error

Counts

125 → 6

Compiler

Compiled 2505 to 1977 computations (21.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))
0.1b	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))
0.2b	(/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9))))
9.3b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))

rewrite266.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

46×	`add-sqr-sqrt_binary64_1464`
38×	`times-frac_binary64_1448`
37×	`*-un-lft-identity_binary64_1442`
35×	`add-cube-cbrt_binary64_1477`
25×	`sqrt-prod_binary64_1458`
24×	`associate-r_binary64_1382`
11×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `flip3--_binary64_1446` `flip--_binary64_1417`
10×	`frac-add_binary64_1450`
9×	`add-log-exp_binary64_1481`
7×	`pow1_binary64_1503`
6×	`frac-times_binary64_1452` `associate-l/_binary64_1385` `sqrt-div_binary64_1459` `associate-/r_binary64_1386`
5×	`associate-l_binary64_1383`
4×	`flip3-+_binary64_1445` `associate-/r/_binary64_1388` `flip-+_binary64_1416` `associate-+l+_binary64_1375`
3×	`unswap-sqr_binary64_1410` `associate-r/_binary64_1384` `associate-/l_binary64_1387` `cancel-sign-sub-inv_binary64_1408`
2×	`div-exp_binary64_1493` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `sum-log_binary64_1533`
1×	`pow-prod-down_binary64_1513` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `*-commutative_binary64_1373` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `diff-log_binary64_1534` `associate-+l-_binary64_1377` `sub-neg_binary64_1435` `+-commutative_binary64_1372`

Counts

4 → 133

Calls

4 calls:

15.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))
8.0ms	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))
6.0ms	(/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9))))
3.0ms	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))

Compiler

Compiled 3890 to 2946 computations (24.3% saved)

series520.0ms (6.9%)

Error

Counts

4 → 24

Calls

4 calls:

237.0ms	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))
133.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))
113.0ms	(/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9))))
15.0ms	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))

Compiler

Compiled 1206 to 998 computations (17.2% saved)

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4962	3481
1	4962	3481

prune208.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	159	4	163

Error

Counts

163 → 4

Compiler

Compiled 3726 to 2812 computations (24.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9)))
0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
0.2b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.2b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))

rewrite821.0ms (11%)

Algorithm

1×	rewrite-expression-head

Error

Rules

372×	`times-frac_binary64_1448`
246×	`*-un-lft-identity_binary64_1442`
244×	`add-sqr-sqrt_binary64_1464`
218×	`sqrt-prod_binary64_1458`
190×	`add-cube-cbrt_binary64_1477`
33×	`associate-/l*_binary64_1387`
26×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
16×	`sqrt-div_binary64_1459` `associate-/r/_binary64_1388`
14×	`associate-/r*_binary64_1386`
13×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
11×	`flip3--_binary64_1446` `flip--_binary64_1417`
9×	`div-inv_binary64_1439`
6×	`pow1_binary64_1503` `add-log-exp_binary64_1481`
5×	`associate-l_binary64_1383`
4×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `flip3-+_binary64_1445` `frac-times_binary64_1452` `flip-+_binary64_1416` `associate-r_binary64_1382`
2×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `distribute-lft-out_binary64_1393`
1×	`associate-/l/_binary64_1389` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `*-commutative_binary64_1373` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 323

Calls

4 calls:

56.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
50.0ms	(+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9)))
15.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 9333 to 7319 computations (21.6% saved)

series473.0ms (6.3%)

Error

Counts

4 → 30

Calls

4 calls:

136.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
129.0ms	(+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9)))
98.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
88.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 1179 to 1029 computations (12.7% saved)

simplify135.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

353 → 353

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4959	8777
1	4959	8777

prune620.0ms (8.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	353	0	353
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	353	4	357

Error

Counts

357 → 4

Compiler

Compiled 8489 to 6479 computations (23.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 (-.f64 (*.f64 a 9) 3)))
0.2b	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 a 9) 3))) (+.f64 -1/3 a))
0.2b	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (-.f64 (*.f64 a 9) 3))) (+.f64 -1/3 a)))
0.3b	(/.f64 1 (-.f64 (*.f64 a 9) 3))

rewrite256.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

42×	`add-sqr-sqrt_binary64_1464`
33×	`*-un-lft-identity_binary64_1442` `sqrt-prod_binary64_1458`
31×	`times-frac_binary64_1448`
29×	`add-cube-cbrt_binary64_1477`
21×	`associate-l_binary64_1383`
15×	`add-exp-log_binary64_1480`
14×	`pow1_binary64_1503`
13×	`add-cbrt-cube_binary64_1478`
9×	`associate-*r/_binary64_1384`
7×	`sqrt-div_binary64_1459`
6×	`associate-/r/_binary64_1388`
5×	`distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-r_binary64_1382`
4×	`add-log-exp_binary64_1481` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `flip3-+_binary64_1445` `frac-times_binary64_1452` `flip-+_binary64_1416` `unswap-sqr_binary64_1410`
3×	`div-inv_binary64_1439` `flip3--_binary64_1446` `flip--_binary64_1417` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455`
2×	`inv-pow_binary64_1527` `pow-flip_binary64_1516` `div-exp_binary64_1493` `associate-l/_binary64_1385` `-commutative_binary64_1373`
1×	`1-exp_binary64_1486` `rec-exp_binary64_1492` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `distribute-lft-out_binary64_1393` `pow1/2_binary64_1522`

Counts

4 → 134

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 a 9) 3))) (+.f64 -1/3 a))
14.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (-.f64 (*.f64 a 9) 3))) (+.f64 -1/3 a)))
6.0ms	(/.f64 1 (-.f64 (*.f64 a 9) 3))
6.0ms	(sqrt.f64 (/.f64 1 (-.f64 (*.f64 a 9) 3)))

Compiler

Compiled 3720 to 3022 computations (18.8% saved)

series229.0ms (3.1%)

Error

Counts

4 → 21

Calls

4 calls:

138.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (-.f64 (*.f64 a 9) 3))) (+.f64 -1/3 a)))
30.0ms	(/.f64 1 (-.f64 (*.f64 a 9) 3))
23.0ms	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 a 9) 3))) (+.f64 -1/3 a))
18.0ms	(sqrt.f64 (/.f64 1 (-.f64 (*.f64 a 9) 3)))

Compiler

Compiled 1061 to 881 computations (17% saved)

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5623	2859

prune208.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	155	4	159

Error

Counts

159 → 4

Compiler

Compiled 3730 to 2969 computations (20.4% saved)

regimes444.0ms (5.9%)

Accuracy

Total 0.1b remaining (98.5%)

Threshold costs 0.1b (98.5%)

Compiler

Compiled 5274 to 4614 computations (12.5% saved)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	236	24
1	236	24

end0.0ms (0%)

sample1.9s (25.8%)

Algorithm

1×

intervals

Results

457.0ms	8000×	body	128	valid
17.0ms	268×	body	128	nan
16.0ms	297×	body	128	invalid

Compiler

Compiled 1342 to 1175 computations (12.4% saved)

Details

analyze342.0ms (4.6%)

sample25.0ms (0.3%)

simplify72.0ms (1%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite188.0ms (2.5%)

series304.0ms (4.1%)

simplify69.0ms (0.9%)

prune162.0ms (2.2%)

localize10.0ms (0.1%)

rewrite266.0ms (3.5%)

series520.0ms (6.9%)

simplify80.0ms (1.1%)

prune208.0ms (2.8%)

localize9.0ms (0.1%)

rewrite821.0ms (11%)

series473.0ms (6.3%)

simplify135.0ms (1.8%)

prune620.0ms (8.3%)

localize14.0ms (0.2%)

rewrite256.0ms (3.4%)

series229.0ms (3.1%)

simplify86.0ms (1.1%)

prune208.0ms (2.8%)

regimes444.0ms (5.9%)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample1.9s (25.8%)

Profiling