Details

analyze327.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample33.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	202×	body	128	valid
5.0ms	13×	body	1024	valid
5.0ms	21×	body	2048	valid
3.0ms	12×	body	4096	valid
1.0ms	6×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify172.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 37.9b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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))
0.9b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64_2204` `add-log-exp_binary64_2182`
7×	`*-un-lft-identity_binary64_2143`
6×	`add-sqr-sqrt_binary64_2165`
5×	`add-cube-cbrt_binary64_2178`
4×	`sqrt-div_binary64_2160` `add-exp-log_binary64_2181` `sqrt-prod_binary64_2159` `flip3-+_binary64_2146` `flip-+_binary64_2117` `add-cbrt-cube_binary64_2179`
3×	`sqrt-pow1_binary64_2161`
2×	`pow1/2_binary64_2223` `+-commutative_binary64_2073` `sum-log_binary64_2234` `associate-*r/_binary64_2085`
1×	`rem-sqrt-square_binary64_2156` `pow-prod-down_binary64_2214` `distribute-lft-out_binary64_2094`

Counts

4 → 51

Calls

4 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	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series366.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

231.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
54.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
45.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
36.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify59.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5005	1040

prune226.0ms (4.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 15.3b

Counts

64 → 7

Compiler

Compiled 3633 to 2244 computations (38.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.4b	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
21.4b	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2165`
14×	`*-un-lft-identity_binary64_2143`
9×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
8×	`pow1_binary64_2204` `add-cube-cbrt_binary64_2178`
7×	`sqrt-prod_binary64_2159`
6×	`add-log-exp_binary64_2182` `associate-/r*_binary64_2087` `difference-of-squares_binary64_2112` `times-frac_binary64_2149`
3×	`sqrt-div_binary64_2160` `distribute-lft-out--_binary64_2095` `cancel-sign-sub-inv_binary64_2109` `sqrt-pow1_binary64_2161`
2×	`pow1/2_binary64_2223` `cbrt-undiv_binary64_2177` `flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `div-exp_binary64_2194`
1×	`rem-sqrt-square_binary64_2156` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `associate-/l_binary64_2088` `div-inv_binary64_2140` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `associate-r/_binary64_2085` `flip3-+_binary64_2146` `flip-+_binary64_2117` `frac-2neg_binary64_2154`

Counts

4 → 73

Calls

4 calls:

13.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
12.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series393.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
103.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
53.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
47.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify55.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4916	1730
1	4916	1730

prune203.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	83	9	92

Merged error: 11.6b

Counts

92 → 9

Compiler

Compiled 4134 to 1988 computations (51.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.4b	(sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite58.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_2165`
25×	`*-un-lft-identity_binary64_2143`
24×	`associate-r_binary64_2083`
19×	`times-frac_binary64_2149`
17×	`add-cube-cbrt_binary64_2178`
13×	`pow1_binary64_2204`
9×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
8×	`sqrt-prod_binary64_2159` `difference-of-squares_binary64_2112`
6×	`add-log-exp_binary64_2182`
4×	`distribute-lft-out--_binary64_2095` `pow-prod-down_binary64_2214` `sqrt-pow1_binary64_2161`
3×	`sqrt-div_binary64_2160` `associate-l_binary64_2084` `associate-*r/_binary64_2085` `cancel-sign-sub-inv_binary64_2109`
2×	`pow1/2_binary64_2223` `flip--_binary64_2118` `associate-/r/_binary64_2089` `cbrt-unprod_binary64_2176` `flip3--_binary64_2147` `prod-exp_binary64_2192` `unswap-sqr_binary64_2111`
1×	`rem-sqrt-square_binary64_2156` `cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `sub-neg_binary64_2136` `div-inv_binary64_2140` `flip3-+_binary64_2146` `flip-+_binary64_2117` `*-commutative_binary64_2074` `div-exp_binary64_2194`

Counts

4 → 88

Calls

4 calls:

21.0ms	(.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
14.0ms	(sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series355.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))))
93.0ms	(.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
51.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
40.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5470	1951

prune171.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	101	8	109

Merged error: 10.7b

Counts

109 → 8

Compiler

Compiled 3712 to 1712 computations (53.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.2b	(sqrt.f64 (.f64 (.f64 im im) 2))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite52.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_2165`
50×	`sqrt-prod_binary64_2159`
38×	`*-un-lft-identity_binary64_2143`
36×	`times-frac_binary64_2149`
26×	`add-cube-cbrt_binary64_2178`
12×	`difference-of-squares_binary64_2112`
11×	`pow1_binary64_2204`
9×	`associate-/r*_binary64_2087`
6×	`add-log-exp_binary64_2182` `distribute-lft-out--_binary64_2095` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
4×	`sqrt-div_binary64_2160` `associate-/l*_binary64_2088` `sqrt-pow1_binary64_2161`
3×	`pow-prod-down_binary64_2214` `cancel-sign-sub-inv_binary64_2109`
2×	`pow1/2_binary64_2223` `flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147`
1×	`rem-sqrt-square_binary64_2156` `cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `sqrt-undiv_binary64_2164` `div-inv_binary64_2140` `flip3-+_binary64_2146` `flip-+_binary64_2117` `div-exp_binary64_2194` `frac-2neg_binary64_2154`

Counts

4 → 108

Calls

4 calls:

17.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
8.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series317.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
52.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
47.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
42.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify85.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5246	3621

prune251.0ms (5.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	118	10	128

Merged error: 7.7b

Counts

128 → 10

Compiler

Compiled 5426 to 2521 computations (53.5% saved)

regimes381.0ms (7.7%)

Compiler: Compiled 1524 to 1052 computations (31% saved)

bsearch78.0ms (1.6%)

Steps

Iters	Range	Point
7	1.0783879871995089e+121	6.321203557273547e+122	5.6392861707035385e+122
7	-9.089728099399469e-302	-5.2137122067099377e-303	-5.2611073750173795e-303
9	-7.879764341688507e+170	-2.5496100832393085e+162	-2.5991937408382053e+162

Iters

Range

Point

1.0783879871995089e+121

6.321203557273547e+122

5.6392861707035385e+122

-9.089728099399469e-302

-5.2137122067099377e-303

-5.2611073750173795e-303

-7.879764341688507e+170

-2.5496100832393085e+162

-2.5991937408382053e+162

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	62	103
1	62	103

end0.0ms (0%)

sample1.2s (23.5%)

Algorithm

1×

intervals

Results

303.0ms	6143×	body	128	valid
152.0ms	495×	body	4096	valid
148.0ms	623×	body	2048	valid
73.0ms	368×	body	1024	valid
34.0ms	247×	body	512	valid
12.0ms	124×	body	256	valid

Compiler

Compiled 318 to 215 computations (32.4% saved)

Details

analyze327.0ms (6.6%)

sample33.0ms (0.7%)

simplify172.0ms (3.5%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite31.0ms (0.6%)

series366.0ms (7.4%)

simplify59.0ms (1.2%)

prune226.0ms (4.6%)

localize14.0ms (0.3%)

rewrite46.0ms (0.9%)

series393.0ms (7.9%)

simplify55.0ms (1.1%)

prune203.0ms (4.1%)

localize13.0ms (0.3%)

rewrite58.0ms (1.2%)

series355.0ms (7.2%)

simplify73.0ms (1.5%)

prune171.0ms (3.4%)

localize13.0ms (0.3%)

rewrite52.0ms (1%)

series317.0ms (6.4%)

simplify85.0ms (1.7%)

prune251.0ms (5.1%)

regimes381.0ms (7.7%)

bsearch78.0ms (1.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (23.5%)

Profiling