Details

analyze407.0ms (5.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	46
1	34	46
0	2	2
1	2	2

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

Symmetry

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample33.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	191×	body	128	valid
7.0ms	24×	body	4096	valid
4.0ms	17×	body	2048	valid
2.0ms	13×	body	1024	valid
1.0ms	8×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune5.0ms (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

Error

40.4b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.2b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite72.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

40.2b

Rules

7×	`pow1_binary64_2867`
6×	`*-un-lft-identity_binary64_2806`
5×	`add-log-exp_binary64_2845` `add-sqr-sqrt_binary64_2828`
4×	`add-cube-cbrt_binary64_2841` `sqrt-div_binary64_2823` `sqrt-prod_binary64_2822`
3×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `sqrt-pow1_binary64_2824` `flip3-+_binary64_2809` `flip-+_binary64_2780`
2×	`pow1/2_binary64_2886` `associate-*r/_binary64_2748`
1×	`rem-sqrt-square_binary64_2819` `pow-prod-down_binary64_2877` `sum-log_binary64_2897` `distribute-lft-out_binary64_2757` `+-commutative_binary64_2736`

Counts

3 → 40

Calls

3 calls:

9.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1030 to 354 computations (65.6% saved)

series357.0ms (4.5%)

Error

8.8b

Counts

3 → 42

Calls

3 calls:

124.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
101.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
89.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1760 to 1517 computations (13.8% saved)

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5177	1328

prune87.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Error

8.3b

Counts

83 → 9

Compiler

Compiled 1564 to 835 computations (46.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite86.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

8.3b

Rules

17×	`add-sqr-sqrt_binary64_2828`
14×	`sqrt-prod_binary64_2822`
12×	`*-un-lft-identity_binary64_2806`
8×	`pow1_binary64_2867` `add-cube-cbrt_binary64_2841`
7×	`associate-r_binary64_2746`
6×	`associate-l_binary64_2747`
5×	`add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
4×	`sqrt-div_binary64_2823` `unswap-sqr_binary64_2774`
3×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `flip3-+_binary64_2809` `flip-+_binary64_2780` `pow-prod-down_binary64_2877`
2×	`associate-*r/_binary64_2748` `distribute-lft-out_binary64_2757`
1×	`rem-sqrt-square_binary64_2819` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `sqrt-unprod_binary64_2826` `*-commutative_binary64_2737` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

3 → 60

Calls

3 calls:

12.0ms	(.f64 (sqrt.f64 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 re re) (.f64 im im)))

Compiler

Compiled 1621 to 565 computations (65.1% saved)

series352.0ms (4.5%)

Error

8.3b

Counts

3 → 42

Calls

3 calls:

126.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
99.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
90.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))

Compiler

Compiled 1839 to 1589 computations (13.6% saved)

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5215	1886

prune102.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	102	9	111

Error

8.3b

Counts

111 → 9

Compiler

Compiled 2145 to 1057 computations (50.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
1.1b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
32.7b	(sqrt.f64 (.f64 2 (.f64 im im)))

rewrite168.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

8.3b

Rules

51×	`add-sqr-sqrt_binary64_2828`
50×	`sqrt-prod_binary64_2822`
38×	`*-un-lft-identity_binary64_2806`
36×	`times-frac_binary64_2812`
26×	`add-cube-cbrt_binary64_2841`
12×	`difference-of-squares_binary64_2775`
11×	`pow1_binary64_2867`
9×	`associate-/r*_binary64_2750`
6×	`add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `distribute-lft-out--_binary64_2758`
4×	`sqrt-pow1_binary64_2824` `sqrt-div_binary64_2823` `associate-/l*_binary64_2751`
3×	`pow-prod-down_binary64_2877` `cancel-sign-sub-inv_binary64_2772`
2×	`pow1/2_binary64_2886` `flip3--_binary64_2810` `flip--_binary64_2781` `associate-/r/_binary64_2752`
1×	`flip3-+_binary64_2809` `flip-+_binary64_2780` `rem-sqrt-square_binary64_2819` `diff-log_binary64_2898` `sub-neg_binary64_2799` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `sqrt-undiv_binary64_2827` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803`

Counts

4 → 108

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3656 to 1176 computations (67.8% saved)

series367.0ms (4.7%)

Error

2.8b

Counts

4 → 40

Calls

4 calls:

112.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
103.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
80.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
32.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 2035 to 1600 computations (21.4% saved)

simplify92.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5583	3957

prune169.0ms (2.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	142	6	148
Fresh	0	6	6
Picked	1	0	1
Done	1	1	2
Total	144	13	157

Error

2.8b

Counts

157 → 13

Compiler

Compiled 4218 to 1660 computations (60.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.3b	(.f64 (sqrt.f64 2) (/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
1.1b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite216.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

2.8b

Rules

91×	`add-sqr-sqrt_binary64_2828`
61×	`sqrt-prod_binary64_2822`
58×	`*-un-lft-identity_binary64_2806` `times-frac_binary64_2812`
42×	`add-cube-cbrt_binary64_2841`
33×	`associate-r_binary64_2746`
16×	`difference-of-squares_binary64_2775`
11×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
9×	`associate-/r*_binary64_2750`
8×	`distribute-lft-out--_binary64_2758`
7×	`pow1_binary64_2867`
6×	`add-log-exp_binary64_2845` `sqrt-div_binary64_2823` `unswap-sqr_binary64_2774` `associate-l_binary64_2747`
4×	`associate-/r/_binary64_2752`
3×	`flip3--_binary64_2810` `flip--_binary64_2781` `cancel-sign-sub-inv_binary64_2772` `associate-/l*_binary64_2751`
2×	`div-exp_binary64_2857` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `cbrt-undiv_binary64_2840` `div-inv_binary64_2803`
1×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `flip3-+_binary64_2809` `flip-+_binary64_2780` `rem-sqrt-square_binary64_2819` `diff-log_binary64_2898` `sub-neg_binary64_2799` `pow-prod-down_binary64_2877` `associate-r/_binary64_2748` `-commutative_binary64_2737` `frac-2neg_binary64_2817` `clear-num_binary64_2805`

Counts

4 → 144

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 2) (/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
11.0ms	(/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 4875 to 1272 computations (73.9% saved)

series447.0ms (5.7%)

Error

0.5b

Counts

4 → 45

Calls

4 calls:

131.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
101.0ms	(.f64 (sqrt.f64 2) (/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
99.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
74.0ms	(/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))

Compiler

Compiled 2349 to 1890 computations (19.5% saved)

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4941	4885
1	4941	4885

prune189.0ms (2.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	189	13	202

Error

0.5b

Counts

202 → 13

Compiler

Compiled 5185 to 1634 computations (68.5% saved)

regimes1.7s (22%)

Accuracy

Total 17.8b remaining (98%)

Threshold costs 0b (0%)

Compiler

Compiled 12931 to 9527 computations (26.3% saved)

bsearch93.0ms (1.2%)

Steps

Iters	Range		Point
7	4.3269733369951136e+95	5.239044031558134e+97	4.484644676042966e+96
9	5.294526901726392e-245	1.0729863024312981e-238	3.1846958944297933e-243
9	-5.2432992766090534e-207	-3.262656210511354e-215	-3.4201707617626984e-214
7	-1.355286484306959e+93	-5.187787891685001e+91	-1.3361067715788965e+93

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	122
1	86	122

Removed

()

end0.0ms (0%)

sample2.6s (33.2%)

Algorithm

1×

intervals

Results

281.0ms	6032×	body	128	valid
156.0ms	659×	body	2048	valid
150.0ms	521×	body	4096	valid
82.0ms	452×	body	1024	valid
29.0ms	220×	body	512	valid
10.0ms	116×	body	256	valid

Compiler

Compiled 1800 to 1329 computations (26.2% saved)

Details

analyze407.0ms (5.2%)

sample33.0ms (0.4%)

simplify7.0ms (0.1%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

rewrite72.0ms (0.9%)

series357.0ms (4.5%)

simplify64.0ms (0.8%)

prune87.0ms (1.1%)

localize11.0ms (0.1%)

rewrite86.0ms (1.1%)

series352.0ms (4.5%)

simplify73.0ms (0.9%)

prune102.0ms (1.3%)

localize12.0ms (0.2%)

rewrite168.0ms (2.1%)

series367.0ms (4.7%)

simplify92.0ms (1.2%)

prune169.0ms (2.1%)

localize15.0ms (0.2%)

rewrite216.0ms (2.7%)

series447.0ms (5.7%)

simplify86.0ms (1.1%)

prune189.0ms (2.4%)

regimes1.7s (22%)

bsearch93.0ms (1.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.6s (33.2%)

Profiling