Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample32.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify169.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

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: 0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_1442`
26×	`add-sqr-sqrt_binary64_1464`
21×	`distribute-lft-out_binary64_1393`
18×	`times-frac_binary64_1448`
15×	`add-cube-cbrt_binary64_1477`
14×	`sqrt-prod_binary64_1458`
6×	`associate-/r*_binary64_1386`
5×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
4×	`pow1_binary64_1503`
3×	`associate-/l*_binary64_1387` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-/r/_binary64_1388` `sqrt-div_binary64_1459`
1×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `pow1/2_binary64_1522` `div-exp_binary64_1493`

Counts

3 → 71

Calls

3 calls:

17.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
12.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
6.0ms	(sqrt.f64 (+.f64 x 1))

series170.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

116.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
29.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
25.0ms	(sqrt.f64 (+.f64 x 1))

simplify104.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4942	1549
1	4942	1549

prune156.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	5	81

Merged error: 0b

Counts

81 → 5

Compiler

Compiled 1358 to 1009 computations (25.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.1b	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
0.2b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

rewrite91.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`*-un-lft-identity_binary64_1442`
156×	`times-frac_binary64_1448`
114×	`add-sqr-sqrt_binary64_1464`
79×	`add-cube-cbrt_binary64_1477`
69×	`distribute-lft-out_binary64_1393`
38×	`sqrt-prod_binary64_1458`
25×	`associate-/r*_binary64_1386`
17×	`add-exp-log_binary64_1480`
11×	`add-cbrt-cube_binary64_1478`
9×	`associate-/l*_binary64_1387`
8×	`div-exp_binary64_1493`
6×	`div-inv_binary64_1439` `add-log-exp_binary64_1481` `pow1_binary64_1503`
4×	`cbrt-undiv_binary64_1476`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-/l/_binary64_1389` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `sqrt-div_binary64_1459` `frac-2neg_binary64_1453`
1×	`sqrt-pow1_binary64_1460` `inv-pow_binary64_1527` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `associate-/r/_binary64_1388` `+-commutative_binary64_1372` `pow-flip_binary64_1516` `pow1/2_binary64_1522`

Counts

4 → 183

Calls

4 calls:

23.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
16.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
12.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
6.0ms	(sqrt.f64 (+.f64 x 1))

series229.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
58.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
28.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
25.0ms	(sqrt.f64 (+.f64 x 1))

simplify181.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4985	4261
1	4985	4261

prune377.0ms (7.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	195	5	200

Merged error: 0b

Counts

200 → 5

Compiler

Compiled 3583 to 2699 computations (24.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1473`
23×	`add-sqr-sqrt_binary64_1464`
15×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
11×	`pow1_binary64_1503`
9×	`pow1/3_binary64_1524`
6×	`associate-r_binary64_1382` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `add-exp-log_binary64_1480`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `unswap-sqr_binary64_1410`
2×	`pow-prod-down_binary64_1513` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512`
1×	`pow2_binary64_1523` `cbrt-unprod_binary64_1475` `pow-plus_binary64_1505` `*-commutative_binary64_1373` `prod-exp_binary64_1491`

Counts

4 → 73

Calls

4 calls:

12.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
2.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)

series680.0ms (13.6%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt.f64 x)
177.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
166.0ms	(cbrt.f64 x)
160.0ms	(cbrt.f64 x)

simplify116.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4892	563
1	4892	563

prune140.0ms (2.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	85	5	90

Merged error: 0b

Counts

90 → 5

Compiler

Compiled 1530 to 850 computations (44.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite113.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`*-un-lft-identity_binary64_1442`
92×	`add-sqr-sqrt_binary64_1464`
79×	`sqrt-prod_binary64_1458`
76×	`times-frac_binary64_1448`
57×	`distribute-lft-out_binary64_1393`
47×	`add-cube-cbrt_binary64_1477`
42×	`associate-r_binary64_1382`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
7×	`pow1_binary64_1503`
6×	`associate-/r_binary64_1386` `associate-/l_binary64_1387` `associate-l_binary64_1383` `add-log-exp_binary64_1481` `unswap-sqr_binary64_1410`
4×	`associate-/r/_binary64_1388` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `sqrt-div_binary64_1459` `prod-exp_binary64_1491` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `clear-num_binary64_1441` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`

Counts

4 → 160

Calls

4 calls:

44.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
19.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
12.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
7.0ms	(sqrt.f64 (+.f64 x 1))

series331.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
107.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
29.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
23.0ms	(sqrt.f64 (+.f64 x 1))

simplify176.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4960	3813
1	4960	3813

prune339.0ms (6.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	172	5	177

Merged error: 0b

Counts

177 → 5

Compiler

Compiled 3639 to 2306 computations (36.6% saved)

regimes136.0ms (2.7%)

Compiler: Compiled 636 to 528 computations (17% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample1.3s (26.2%)

Algorithm

1×

intervals

Results

428.0ms	7995×	body	128	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 326 to 272 computations (16.6% saved)

Details

analyze6.0ms (0.1%)

sample32.0ms (0.6%)

simplify169.0ms (3.4%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite45.0ms (0.9%)

series170.0ms (3.4%)

simplify104.0ms (2.1%)

prune156.0ms (3.1%)

localize13.0ms (0.3%)

rewrite91.0ms (1.8%)

series229.0ms (4.6%)

simplify181.0ms (3.6%)

prune377.0ms (7.6%)

localize17.0ms (0.3%)

rewrite28.0ms (0.6%)

series680.0ms (13.6%)

simplify116.0ms (2.3%)

prune140.0ms (2.8%)

localize15.0ms (0.3%)

rewrite113.0ms (2.3%)

series331.0ms (6.6%)

simplify176.0ms (3.5%)

prune339.0ms (6.8%)

regimes136.0ms (2.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (26.2%)

Profiling