Details

analyze335.0ms (5.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample37.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	190×	body	128	valid
7.0ms	31×	body	2048	valid
4.0ms	14×	body	4096	valid
4.0ms	256×	pre	128	true
2.0ms	11×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify120.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

prune3.0ms (0%)

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

38.9b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize11.0ms (0.2%)

Local error

Found 8 expressions with local error:

28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
1.0b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.0b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_426`
8×	`pow1_binary64_465` `*-un-lft-identity_binary64_404` `add-log-exp_binary64_443`
6×	`add-cube-cbrt_binary64_439`
5×	`sqrt-prod_binary64_420`
4×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442` `sqrt-div_binary64_421`
3×	`cancel-sign-sub-inv_binary64_370` `sqrt-pow1_binary64_422`
2×	`pow1/2_binary64_484` `associate-*r/_binary64_346` `flip3-+_binary64_407` `flip3--_binary64_408` `difference-of-squares_binary64_373` `flip-+_binary64_378` `flip--_binary64_379`
1×	`pow-prod-down_binary64_475` `sum-log_binary64_495` `distribute-lft-out--_binary64_356` `diff-log_binary64_496` `sub-neg_binary64_397` `+-commutative_binary64_334` `rem-sqrt-square_binary64_417`

Counts

4 → 56

Calls

8 calls:

10.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

series368.0ms (5.9%)

Counts

4 → 47

Calls

4 calls:

101.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
91.0ms	(+.f64 (.f64 re re) (.f64 im im))
90.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
86.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Compiler

Compiled 1248 to 1149 computations (7.9% saved)

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5153	1539

prune140.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Error

0.5b

Counts

104 → 7

Compiler

Compiled 1915 to 945 computations (50.7% saved)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune6.0ms (0.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	1	1
Total	7	7

Error

0.5b

Counts

7 → 7

Compiler

Compiled 73 to 66 computations (9.6% saved)

localize17.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.1b	(sqrt.f64 (/.f64 1 im))
0.0b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))))
0.0b	(.f64 1/2 (.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))))
0.1b	(sqrt.f64 (/.f64 1 im))
0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.4b	(*.f64 re (sqrt.f64 2))
0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_426`
40×	`sqrt-prod_binary64_420`
28×	`associate-r_binary64_344`
27×	`*-un-lft-identity_binary64_404`
26×	`add-cube-cbrt_binary64_439`
20×	`times-frac_binary64_410`
17×	`pow1_binary64_465`
13×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
10×	`associate-l_binary64_345`
7×	`pow-prod-down_binary64_475`
6×	`unswap-sqr_binary64_372`
5×	`sqrt-pow1_binary64_422` `prod-exp_binary64_453` `cbrt-unprod_binary64_437`
4×	`add-log-exp_binary64_443`
3×	`pow1/2_binary64_484` `*-commutative_binary64_335` `rem-sqrt-square_binary64_417`
2×	`div-inv_binary64_401` `sqrt-div_binary64_421`
1×	`pow-flip_binary64_478` `sqrt-unprod_binary64_424` `associate-*r/_binary64_346` `inv-pow_binary64_489`

Counts

4 → 112

Calls

8 calls:

11.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
6.0ms	(*.f64 re (sqrt.f64 2))
3.0ms	(sqrt.f64 (/.f64 1 im))
0.0ms	(.f64 1/2 (.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))))

series163.0ms (2.6%)

Counts

4 → 15

Calls

4 calls:

89.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
36.0ms	(*.f64 re (sqrt.f64 2))
23.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
14.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 640 to 597 computations (6.7% saved)

simplify92.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5027	1398

prune180.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	127	7	134

Error

0.5b

Counts

134 → 7

Compiler

Compiled 2982 to 2352 computations (21.1% saved)

localize16.0ms (0.3%)

Local error

Found 8 expressions with local error:

1.9b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))
0.0b	(.f64 (.f64 im im) 2)
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))
1.9b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.4b	(sqrt.f64 (.f64 (.f64 im im) 2))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64_404`
32×	`sqrt-prod_binary64_420`
28×	`times-frac_binary64_410`
24×	`add-sqr-sqrt_binary64_426`
23×	`add-cube-cbrt_binary64_439`
11×	`pow1_binary64_465`
7×	`associate-/r*_binary64_348`
6×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442` `add-log-exp_binary64_443` `distribute-lft-out_binary64_355`
4×	`sqrt-pow1_binary64_422` `sqrt-div_binary64_421` `associate-/l*_binary64_349`
3×	`pow-prod-down_binary64_475` `flip3-+_binary64_407` `flip-+_binary64_378`
2×	`pow1/2_binary64_484` `associate-/r/_binary64_350`
1×	`div-exp_binary64_455` `sqrt-undiv_binary64_425` `frac-2neg_binary64_415` `div-inv_binary64_401` `sum-log_binary64_495` `clear-num_binary64_403` `cbrt-undiv_binary64_438` `+-commutative_binary64_334` `rem-sqrt-square_binary64_417`

Counts

4 → 93

Calls

8 calls:

14.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))
6.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))

series333.0ms (5.3%)

Counts

4 → 39

Calls

4 calls:

118.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))
94.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
91.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
30.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

Compiler

Compiled 1333 to 1137 computations (14.7% saved)

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5005	3293

prune291.0ms (4.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	129	10	139

Error

0.4b

Counts

139 → 10

Compiler

Compiled 3452 to 1376 computations (60.1% saved)

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	414	988
1	414	988

regimes412.0ms (6.6%)

Accuracy

Total 11.0b remaining (96.7%)

Threshold costs 0b (0%)

Compiler

Compiled 2280 to 1711 computations (25% saved)

bsearch92.0ms (1.5%)

Steps

Iters	Range		Point
5	5.04333785509281e+147	1.9666952028333115e+148	1.9275280704393263e+148
7	8.53393460939042e-152	1.2045945320046373e-149	1.2142340433856673e-151
8	-4.30769696463379e-126	-2.2803129884361567e-130	-4.253390744375976e-130
10	-1.4704838418747468e+131	-2.5136733106042e+120	-1.937472551084114e+129

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	77	123
1	77	123

end0.0ms (0%)

sample3.4s (53.6%)

Algorithm

1×

intervals

Results

284.0ms	6102×	body	128	valid
150.0ms	661×	body	2048	valid
147.0ms	516×	body	4096	valid
117.0ms	8000×	pre	128	true
77.0ms	416×	body	1024	valid
28.0ms	213×	body	512	valid
8.0ms	92×	body	256	valid

Compiler

Compiled 2077 to 1560 computations (24.9% saved)

Pareto

-0.20185290059342487

Details

analyze335.0ms (5.4%)

sample37.0ms (0.6%)

simplify120.0ms (1.9%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite32.0ms (0.5%)

series368.0ms (5.9%)

simplify74.0ms (1.2%)

prune140.0ms (2.2%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune6.0ms (0.1%)

localize17.0ms (0.3%)

rewrite38.0ms (0.6%)

series163.0ms (2.6%)

simplify92.0ms (1.5%)

prune180.0ms (2.9%)

localize16.0ms (0.3%)

rewrite38.0ms (0.6%)

series333.0ms (5.3%)

simplify79.0ms (1.3%)

prune291.0ms (4.6%)

simplify17.0ms (0.3%)

regimes412.0ms (6.6%)

bsearch92.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.4s (53.6%)

Profiling