Details

analyze95.0ms (1.2%)

Algorithm

1×

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)

sample39.0ms (0.5%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
1.0ms	8×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify170.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

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

Merged error: 0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.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)))

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

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

Counts

4 → 99

Calls

4 calls:

28.0ms	(.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))

series185.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
53.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
31.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
26.0ms	(*.f64 (-.f64 a 1/3) 9)

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4954	2236
1	4954	2236

prune185.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	106	7	113

Merged error: 0.0b

Counts

113 → 7

Compiler

Compiled 2592 to 2016 computations (22.2% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite113.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`add-sqr-sqrt_binary64_1464`
106×	`times-frac_binary64_1448`
86×	`sqrt-prod_binary64_1458`
71×	`*-un-lft-identity_binary64_1442`
65×	`add-cube-cbrt_binary64_1477`
32×	`add-exp-log_binary64_1480`
27×	`associate-r_binary64_1382` `associate-l_binary64_1383`
20×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459`
15×	`pow1_binary64_1503` `unswap-sqr_binary64_1410`
14×	`associate-/r*_binary64_1386`
12×	`sqrt-pow1_binary64_1460`
11×	`associate-*l/_binary64_1385` `div-exp_binary64_1493`
8×	`associate-/r/_binary64_1388` `prod-exp_binary64_1491`
6×	`cbrt-undiv_binary64_1476` `associate-/l*_binary64_1387` `pow-flip_binary64_1516`
5×	`flip3--_binary64_1446` `flip--_binary64_1417`
4×	`cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `add-log-exp_binary64_1481` `pow1/2_binary64_1522`
3×	`1-exp_binary64_1486` `pow-prod-down_binary64_1513` `rec-exp_binary64_1492`
2×	`clear-num_binary64_1441` `frac-2neg_binary64_1453`
1×	`associate-r/_binary64_1384` `inv-pow_binary64_1527` `rem-sqrt-square_binary64_1455` `-commutative_binary64_1373` `frac-times_binary64_1452`

Counts

4 → 211

Calls

4 calls:

38.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
17.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
16.0ms	(/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
6.0ms	(sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

series313.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
91.0ms	(/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
47.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
37.0ms	(sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

simplify185.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4941	5862
1	4941	5862

prune798.0ms (9.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	223	7	230

Merged error: 0.0b

Counts

230 → 7

Compiler

Compiled 7579 to 6247 computations (17.6% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.1b	(.f64 (+.f64 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (+.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))

rewrite106.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
36×	`cancel-sign-sub-inv_binary64_1408`
35×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
32×	`frac-times_binary64_1452`
31×	`sqrt-prod_binary64_1458`
28×	`add-cube-cbrt_binary64_1477`
21×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
16×	`associate-*r/_binary64_1384`
14×	`flip3--_binary64_1446` `flip--_binary64_1417` `pow1_binary64_1503` `associate-*l/_binary64_1385`
13×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
12×	`times-frac_binary64_1448`
10×	`associate-r_binary64_1382`
9×	`associate-l_binary64_1383`
6×	`sub-neg_binary64_1435`
5×	`pow-prod-down_binary64_1513`
4×	`associate-/r*_binary64_1386` `cbrt-unprod_binary64_1475` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411`
3×	`associate-/l*_binary64_1387` `distribute-lft-out_binary64_1393`
2×	`sqrt-pow1_binary64_1460` `associate-/r/_binary64_1388` `*-commutative_binary64_1373` `distribute-lft-out--_binary64_1394`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`

Counts

4 → 167

Calls

4 calls:

39.0ms	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (+.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
25.0ms	(.f64 (+.f64 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series462.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (+.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
120.0ms	(.f64 (+.f64 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
100.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
29.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify185.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5005	6839

prune598.0ms (7.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	179	7	186

Merged error: 0.0b

Counts

186 → 7

Compiler

Compiled 6363 to 4715 computations (25.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3)) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
0.2b	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
0.3b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
0.4b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (+.f64 (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3)) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))

rewrite172.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

111×	`add-sqr-sqrt_binary64_1464`
84×	`*-un-lft-identity_binary64_1442`
70×	`times-frac_binary64_1448`
65×	`sqrt-prod_binary64_1458`
58×	`add-cube-cbrt_binary64_1477`
38×	`associate-l_binary64_1383`
37×	`add-exp-log_binary64_1480`
36×	`cancel-sign-sub-inv_binary64_1408`
35×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
33×	`frac-times_binary64_1452`
25×	`add-cbrt-cube_binary64_1478`
23×	`associate-r_binary64_1382`
21×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
17×	`associate-*r/_binary64_1384`
15×	`pow1_binary64_1503`
14×	`flip3--_binary64_1446` `flip--_binary64_1417`
12×	`prod-exp_binary64_1491`
11×	`difference-of-squares_binary64_1411` `associate-*l/_binary64_1385` `unswap-sqr_binary64_1410`
10×	`div-exp_binary64_1493`
9×	`distribute-lft-out--_binary64_1394`
8×	`associate-/r*_binary64_1386` `cbrt-unprod_binary64_1475`
6×	`sub-neg_binary64_1435`
5×	`cbrt-undiv_binary64_1476` `pow-prod-down_binary64_1513`
4×	`associate-/r/_binary64_1388` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481`
3×	`div-inv_binary64_1439` `associate-/l_binary64_1387` `1-exp_binary64_1486` `-commutative_binary64_1373` `rec-exp_binary64_1492` `pow-flip_binary64_1516`
2×	`distribute-lft-out_binary64_1393`
1×	`sqrt-pow1_binary64_1460` `inv-pow_binary64_1527` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`

Counts

4 → 252

Calls

4 calls:

47.0ms	(.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3)) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
33.0ms	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (+.f64 (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3)) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
31.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
15.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))

series564.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

330.0ms	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (+.f64 (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3)) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
114.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
99.0ms	(.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3)) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
20.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5345	8433

prune936.0ms (11.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	264	0	264
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	264	7	271

Merged error: 0.0b

Counts

271 → 7

Compiler

Compiled 9108 to 6881 computations (24.5% saved)

regimes483.0ms (5.9%)

Compiler: Compiled 3806 to 3302 computations (13.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms (0%)

sample2.3s (27.7%)

Algorithm

1×

intervals

Results

749.0ms	8000×	body	128	valid
26.0ms	261×	body	128	invalid
24.0ms	282×	body	128	nan

Compiler

Compiled 975 to 847 computations (13.1% saved)

Details

analyze95.0ms (1.2%)

sample39.0ms (0.5%)

simplify170.0ms (2.1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

rewrite57.0ms (0.7%)

series185.0ms (2.3%)

simplify63.0ms (0.8%)

prune185.0ms (2.3%)

localize20.0ms (0.3%)

rewrite113.0ms (1.4%)

series313.0ms (3.8%)

simplify185.0ms (2.3%)

prune798.0ms (9.8%)

localize27.0ms (0.3%)

rewrite106.0ms (1.3%)

series462.0ms (5.7%)

simplify185.0ms (2.3%)

prune598.0ms (7.3%)

localize15.0ms (0.2%)

rewrite172.0ms (2.1%)

series564.0ms (6.9%)

simplify99.0ms (1.2%)

prune936.0ms (11.5%)

regimes483.0ms (5.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.3s (27.7%)

Profiling