Details

analyze7.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 20 computations (31% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify142.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5047	13

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

0.0b

Counts

2 → 2

Compiler

Compiled 43 to 33 computations (23.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.4b	(/.f64 1 (*.f64 i i))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_1464`
35×	`times-frac_binary64_1448`
33×	`*-un-lft-identity_binary64_1442`
17×	`add-cube-cbrt_binary64_1477`
15×	`add-exp-log_binary64_1480`
12×	`difference-of-squares_binary64_1411`
10×	`pow1_binary64_1503`
9×	`associate-/r*_binary64_1386` `add-cbrt-cube_binary64_1478`
8×	`distribute-lft-out--_binary64_1394`
6×	`div-inv_binary64_1439` `associate-/l*_binary64_1387` `pow-flip_binary64_1516`
5×	`div-exp_binary64_1493`
3×	`cbrt-undiv_binary64_1476` `prod-exp_binary64_1491`
2×	`associate-/r/_binary64_1388` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `add-log-exp_binary64_1481` `frac-2neg_binary64_1453`
1×	`pow2_binary64_1523` `inv-pow_binary64_1527` `cbrt-unprod_binary64_1475` `pow-plus_binary64_1505` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `pow-sqr_binary64_1415` `flip--_binary64_1417` `pow-prod-up_binary64_1512`

Counts

2 → 81

Calls

2 calls:

8.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(/.f64 1 (*.f64 i i))

series31.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

18.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
13.0ms	(/.f64 1 (*.f64 i i))

simplify75.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5049	1212

prune81.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	86	3	89

Error

Counts

89 → 3

Compiler

Compiled 1231 to 942 computations (23.5% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
0.1b	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
0.4b	(/.f64 1 (*.f64 i i))
28.8b	(sqrt.f64 (/.f64 1 (*.f64 i i)))

rewrite100.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

528×	`times-frac_binary64_1448`
424×	`add-sqr-sqrt_binary64_1464`
388×	`*-un-lft-identity_binary64_1442`
273×	`sqrt-prod_binary64_1458`
156×	`add-cube-cbrt_binary64_1477`
152×	`difference-of-squares_binary64_1411`
57×	`distribute-lft-out--_binary64_1394`
49×	`distribute-lft-out_binary64_1393`
38×	`div-inv_binary64_1439`
34×	`associate-/r/_binary64_1388`
24×	`associate-/l*_binary64_1387`
22×	`add-exp-log_binary64_1480`
21×	`pow1_binary64_1503`
19×	`associate-/r*_binary64_1386`
16×	`add-cbrt-cube_binary64_1478` `flip3-+_binary64_1445` `flip-+_binary64_1416`
12×	`pow-flip_binary64_1516`
8×	`sqrt-pow1_binary64_1460` `div-exp_binary64_1493`
6×	`cbrt-undiv_binary64_1476`
4×	`add-log-exp_binary64_1481`
3×	`rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `prod-exp_binary64_1491`
2×	`pow2_binary64_1523` `inv-pow_binary64_1527` `pow-plus_binary64_1505` `1-exp_binary64_1486` `pow-prod-down_binary64_1513` `rec-exp_binary64_1492` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512`
1×	`cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `pow1/2_binary64_1522`

Counts

4 → 393

Calls

4 calls:

25.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
5.0ms	(/.f64 1 (*.f64 i i))
5.0ms	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
5.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))

series106.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
37.0ms	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
12.0ms	(/.f64 1 (*.f64 i i))
5.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))

simplify180.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5181	15009

prune1.1s (34.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	405	0	405
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	405	3	408

Error

Counts

408 → 3

Compiler

Compiled 11663 to 10163 computations (12.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (pow.f64 i 6) -4) (-.f64 (.f64 (*.f64 i i) -1/4) (pow.f64 i 4)))
0.0b	(*.f64 (pow.f64 i 6) -4)
0.0b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
0.2b	(.f64 (.f64 i i) -1/4)

rewrite37.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1464`
14×	`cancel-sign-sub-inv_binary64_1408` `add-exp-log_binary64_1480`
12×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
11×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481`
10×	`unpow-prod-down_binary64_1521`
9×	`pow1_binary64_1503`
8×	`associate-l_binary64_1383` `associate-+r+_binary64_1374`
6×	`associate-r_binary64_1382` `prod-exp_binary64_1491`
4×	`cbrt-unprod_binary64_1475` `sqr-pow_binary64_1414` `unswap-sqr_binary64_1410`
3×	`pow-prod-down_binary64_1513`
2×	`sum-log_binary64_1533` `sub-neg_binary64_1435` `*-commutative_binary64_1373` `diff-log_binary64_1534`
1×	`associate-+r-_binary64_1376` `pow-exp_binary64_1510` `flip3--_binary64_1446` `+-commutative_binary64_1372` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-to-exp_binary64_1511`

Counts

4 → 83

Calls

4 calls:

12.0ms	(+.f64 (.f64 (pow.f64 i 6) -4) (-.f64 (.f64 (*.f64 i i) -1/4) (pow.f64 i 4)))
7.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
6.0ms	(.f64 (.f64 i i) -1/4)
5.0ms	(*.f64 (pow.f64 i 6) -4)

series148.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
33.0ms	(+.f64 (.f64 (pow.f64 i 6) -4) (-.f64 (.f64 (*.f64 i i) -1/4) (pow.f64 i 4)))
31.0ms	(*.f64 (pow.f64 i 6) -4)
18.0ms	(.f64 (.f64 i i) -1/4)

simplify90.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4911	1317
1	4911	1317

prune100.0ms (3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	95	3	98

Error

Counts

98 → 3

Compiler

Compiled 1865 to 1299 computations (30.3% saved)

regimes50.0ms (1.5%)

Accuracy

Total 0.3b remaining (99.9%)

Threshold costs 0.3b (99.9%)

Compiler

Compiled 488 to 416 computations (14.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	13
1	30	13

end0.0ms (0%)

sample947.0ms (28.5%)

Algorithm

1×

intervals

Results

450.0ms	8000×	body	128	valid
103.0ms	8000×	pre	128	true

Compiler

Compiled 256 to 219 computations (14.5% saved)

Details

analyze7.0ms (0.2%)

sample24.0ms (0.7%)

simplify142.0ms (4.3%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

rewrite19.0ms (0.6%)

series31.0ms (0.9%)

simplify75.0ms (2.3%)

prune81.0ms (2.4%)

localize13.0ms (0.4%)

rewrite100.0ms (3%)

series106.0ms (3.2%)

simplify180.0ms (5.4%)

prune1.1s (34.5%)

localize10.0ms (0.3%)

rewrite37.0ms (1.1%)

series148.0ms (4.5%)

simplify90.0ms (2.7%)

prune100.0ms (3%)

regimes50.0ms (1.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample947.0ms (28.5%)

Profiling