Details

analyze8.0ms (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)

sample26.0ms (0.6%)

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 (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5047	13

prune6.0ms (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

0.6b

Counts

2 → 2

Compiler

Compiled 43 to 33 computations (23.3% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.4b	(/.f64 1 (*.f64 i i))
0.4b	(/.f64 1 (*.f64 i i))
0.7b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_1123`
35×	`times-frac_binary64_1107`
33×	`*-un-lft-identity_binary64_1101`
17×	`add-cube-cbrt_binary64_1136`
15×	`add-exp-log_binary64_1139`
12×	`difference-of-squares_binary64_1070`
10×	`pow1_binary64_1162`
9×	`add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
8×	`distribute-lft-out--_binary64_1053`
6×	`div-inv_binary64_1098` `associate-/l*_binary64_1046` `pow-flip_binary64_1175`
5×	`div-exp_binary64_1152`
3×	`prod-exp_binary64_1150` `cbrt-undiv_binary64_1135`
2×	`1-exp_binary64_1145` `add-log-exp_binary64_1140` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r/_binary64_1047` `rec-exp_binary64_1151`
1×	`inv-pow_binary64_1186` `pow-plus_binary64_1164` `cbrt-unprod_binary64_1134` `pow-prod-up_binary64_1171` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172` `pow2_binary64_1182`

Counts

2 → 81

Calls

4 calls:

9.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(/.f64 1 (*.f64 i i))
0.0ms	(/.f64 1 (*.f64 i i))
0.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

series64.0ms (1.4%)

Counts

2 → 13

Calls

2 calls:

45.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
19.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 211 to 201 computations (4.7% saved)

simplify72.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4880	1285
1	4880	1285

prune103.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	92	4	96

Error

Counts

96 → 4

Compiler

Compiled 1287 to 980 computations (23.9% saved)

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.0b	(+.f64 2 (/.f64 1 i))
0.0b	(+.f64 2 (/.f64 1 i))
0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

rewrite80.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-sqr-sqrt_binary64_1123`
100×	`*-un-lft-identity_binary64_1101`
96×	`times-frac_binary64_1107`
48×	`add-cube-cbrt_binary64_1136`
30×	`associate-r_binary64_1041`
21×	`difference-of-squares_binary64_1070` `associate-l_binary64_1042`
20×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
19×	`div-inv_binary64_1098`
16×	`distribute-lft-out_binary64_1052`
14×	`distribute-lft-out--_binary64_1053`
13×	`associate-/r*_binary64_1045`
8×	`associate-/r/_binary64_1047`
6×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `associate-/l*_binary64_1046` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
4×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `unswap-sqr_binary64_1069`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105`
1×	`-commutative_binary64_1032` `frac-times_binary64_1111` `sum-log_binary64_1192` `associate-r/_binary64_1043` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `associate-*l/_binary64_1044`

Counts

4 → 174

Calls

8 calls:

35.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
9.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
9.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
7.0ms	(+.f64 2 (/.f64 1 i))
0.0ms	(+.f64 2 (/.f64 1 i))

series128.0ms (2.9%)

Counts

4 → 40

Calls

4 calls:

54.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
29.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
29.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
17.0ms	(+.f64 2 (/.f64 1 i))

Compiler

Compiled 745 to 684 computations (8.2% saved)

simplify96.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4931	3805
1	4931	3805

prune277.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	214	4	218

Error

Counts

218 → 4

Compiler

Compiled 4481 to 3864 computations (13.8% saved)

localize16.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.4b	(/.f64 1 (*.f64 i i))
0.1b	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
0.1b	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
0.0b	(+.f64 2 (fabs.f64 (/.f64 1 i)))
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))
31.3b	(sqrt.f64 (/.f64 1 (*.f64 i i)))

rewrite104.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

528×	`times-frac_binary64_1107`
424×	`add-sqr-sqrt_binary64_1123`
388×	`*-un-lft-identity_binary64_1101`
273×	`sqrt-prod_binary64_1117`
156×	`add-cube-cbrt_binary64_1136`
152×	`difference-of-squares_binary64_1070`
57×	`distribute-lft-out--_binary64_1053`
49×	`distribute-lft-out_binary64_1052`
38×	`div-inv_binary64_1098`
34×	`associate-/r/_binary64_1047`
24×	`associate-/l*_binary64_1046`
22×	`add-exp-log_binary64_1139`
21×	`pow1_binary64_1162`
19×	`associate-/r*_binary64_1045`
16×	`flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `flip-+_binary64_1075`
12×	`pow-flip_binary64_1175`
8×	`sqrt-pow1_binary64_1119` `div-exp_binary64_1152`
6×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140`
3×	`rem-sqrt-square_binary64_1114` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
2×	`inv-pow_binary64_1186` `pow-plus_binary64_1164` `1-exp_binary64_1145` `pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `rec-exp_binary64_1151` `pow-prod-down_binary64_1172` `pow2_binary64_1182`
1×	`cbrt-unprod_binary64_1134` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `pow1/2_binary64_1181`

Counts

4 → 393

Calls

8 calls:

23.0ms	(/.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 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
5.0ms	(/.f64 1 (*.f64 i i))
5.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))
0.0ms	(+.f64 2 (fabs.f64 (/.f64 1 i)))

series244.0ms (5.5%)

Counts

4 → 19

Calls

4 calls:

168.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
45.0ms	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
19.0ms	(/.f64 1 (*.f64 i i))
12.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))

Compiler

Compiled 828 to 740 computations (10.6% saved)

simplify186.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

412 → 412

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4923	15548
1	4923	15548

prune1.3s (28.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	412	0	412
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	412	4	416

Error

Counts

416 → 4

Compiler

Compiled 12002 to 10440 computations (13% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 (.f64 i i) -1/4)
0.0b	(.f64 (.f64 i i) -1/4)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
3×	`add-sqr-sqrt_binary64_1123` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-r_binary64_1041` `pow-prod-down_binary64_1172`
2×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
1×	`-commutative_binary64_1032` `add-log-exp_binary64_1140` `associate-l*_binary64_1042` `unswap-sqr_binary64_1069`

Counts

1 → 19

Calls

2 calls:

6.0ms	(.f64 (.f64 i i) -1/4)
0.0ms	(.f64 (.f64 i i) -1/4)

series24.0ms (0.5%)

Counts

1 → 3

Calls

1 calls:

24.0ms

(*.f64 (*.f64 i i) -1/4)

Compiler

Compiled 30 to 30 computations (0% saved)

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5391	182

prune13.0ms (0.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	22	4	26

Error

Counts

26 → 4

Compiler

Compiled 167 to 103 computations (38.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	148	363
1	148	363

regimes78.0ms (1.7%)

Compiler: Compiled 621 to 533 computations (14.2% saved)

bsearch0.0ms (0%)

regimes18.0ms (0.4%)

Compiler: Compiled 76 to 72 computations (5.3% saved)

bsearch0.0ms (0%)

regimes18.0ms (0.4%)

Compiler: Compiled 63 to 60 computations (4.8% saved)

bsearch0.0ms (0%)

regimes12.0ms (0.3%)

Compiler: Compiled 32 to 32 computations (0% saved)

bsearch0.0ms (0%)

regimes19.0ms (0.4%)

Compiler: Compiled 23 to 24 computations (-4.3% saved)

bsearch19.0ms (0.4%)

Steps

Iters	Range		Point
8	0.1437154499146759	3027.709770242239	0.5123809118653021

Compiler

Compiled 1 to 1 computations (0% saved)

regimes16.0ms (0.4%)

Compiler: Compiled 16 to 18 computations (-12.5% saved)

bsearch18.0ms (0.4%)

Steps

Iters	Range		Point
8	0.1437154499146759	3027.709770242239	0.5123809118653021

Compiler

Compiled 1 to 1 computations (0% saved)

regimes14.0ms (0.3%)

Compiler: Compiled 11 to 14 computations (-27.3% saved)

bsearch16.0ms (0.4%)

Steps

Iters	Range		Point
8	0.1437154499146759	3027.709770242239	0.5123809118653021

Compiler

Compiled 1 to 1 computations (0% saved)

regimes15.0ms (0.3%)

Compiler: Compiled 6 to 10 computations (-66.7% saved)

bsearch16.0ms (0.4%)

Steps

Iters	Range		Point
8	0.1437154499146759	3027.709770242239	0.5123809118653021

Compiler

Compiled 1 to 1 computations (0% saved)

regimes12.0ms (0.3%)

Accuracy

Total 0.1b remaining (99.4%)

Threshold costs 0.1b (99.4%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch24.0ms (0.5%)

Steps

Iters	Range		Point
8	0.1437154499146759	3027.709770242239	0.5123809118653021

Compiler

Compiled 96 to 85 computations (11.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	135
1	73	135

end0.0ms (0%)

sample1.2s (26%)

Algorithm

1×

intervals

Results

453.0ms	8000×	body	128	valid
102.0ms	8000×	pre	128	true

Compiler

Compiled 369 to 324 computations (12.2% saved)

Pareto

0.3789468308634168

Details

analyze8.0ms (0.2%)

sample26.0ms (0.6%)

simplify142.0ms (3.2%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

rewrite20.0ms (0.5%)

series64.0ms (1.4%)

simplify72.0ms (1.6%)

prune103.0ms (2.3%)

localize8.0ms (0.2%)

rewrite80.0ms (1.8%)

series128.0ms (2.9%)

simplify96.0ms (2.1%)

prune277.0ms (6.2%)

localize16.0ms (0.3%)

rewrite104.0ms (2.3%)

series244.0ms (5.5%)

simplify186.0ms (4.2%)

prune1.3s (28.7%)

localize3.0ms (0.1%)

rewrite7.0ms (0.2%)

series24.0ms (0.5%)

simplify80.0ms (1.8%)

prune13.0ms (0.3%)

simplify9.0ms (0.2%)

regimes78.0ms (1.7%)

bsearch0.0ms (0%)

regimes18.0ms (0.4%)

bsearch0.0ms (0%)

regimes18.0ms (0.4%)

bsearch0.0ms (0%)

regimes12.0ms (0.3%)

bsearch0.0ms (0%)

regimes19.0ms (0.4%)

bsearch19.0ms (0.4%)

regimes16.0ms (0.4%)

bsearch18.0ms (0.4%)

regimes14.0ms (0.3%)

bsearch16.0ms (0.4%)

regimes15.0ms (0.3%)

bsearch16.0ms (0.4%)

regimes12.0ms (0.3%)

bsearch24.0ms (0.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (26%)

Profiling