Details

analyze414.0ms (4.3%)

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample29.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	209×	body	128	valid
4.0ms	20×	body	2048	valid
3.0ms	11×	body	4096	valid
1.0ms	7×	body	512	valid
1.0ms	5×	body	1024	valid
0.0ms	4×	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

prune3.0ms (0%)

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

35.6b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)))
0.8b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite97.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

35.4b

Rules

8×	`pow1_binary64_2526` `add-log-exp_binary64_2504`
7×	`*-un-lft-identity_binary64_2465`
6×	`add-sqr-sqrt_binary64_2487`
5×	`add-cube-cbrt_binary64_2500`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `flip3-+_binary64_2468` `sqrt-div_binary64_2482` `flip-+_binary64_2439` `sqrt-prod_binary64_2481`
3×	`sqrt-pow1_binary64_2483`
2×	`pow1/2_binary64_2545` `sum-log_binary64_2556` `+-commutative_binary64_2395` `associate-*r/_binary64_2407`
1×	`rem-sqrt-square_binary64_2478` `distribute-lft-out_binary64_2416` `pow-prod-down_binary64_2536`

Counts

4 → 51

Calls

4 calls:

10.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
9.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1296 to 455 computations (64.9% saved)

series341.0ms (3.6%)

Error

5.1b

Counts

4 → 45

Calls

4 calls:

89.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
85.0ms	(+.f64 (.f64 re re) (.f64 im im))
65.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
59.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Compiler

Compiled 1671 to 1467 computations (12.2% saved)

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5033	1373

prune95.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	87	9	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	9	97

Error

4.8b

Counts

97 → 9

Compiler

Compiled 1784 to 890 computations (50.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.8b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite86.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

10×	`*-un-lft-identity_binary64_2465`
8×	`add-log-exp_binary64_2504` `add-sqr-sqrt_binary64_2487`
6×	`pow1_binary64_2526` `add-cube-cbrt_binary64_2500` `sqrt-prod_binary64_2481`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `flip3-+_binary64_2468` `sqrt-div_binary64_2482` `flip-+_binary64_2439`
2×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `sum-log_binary64_2556` `distribute-lft-out_binary64_2416` `+-commutative_binary64_2395`

Counts

4 → 54

Calls

4 calls:

7.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
6.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2066 to 500 computations (75.8% saved)

series408.0ms (4.3%)

Error

4.8b

Counts

4 → 52

Calls

4 calls:

106.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
104.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
74.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
73.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))

Compiler

Compiled 3614 to 2357 computations (34.8% saved)

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4983	1532
1	4983	1532

prune120.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	106	9	115

Error

4.8b

Counts

115 → 9

Compiler

Compiled 3334 to 1137 computations (65.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
26.6b	(sqrt.f64 (.f64 2 (.f64 im im)))
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite177.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

51×	`add-sqr-sqrt_binary64_2487`
50×	`sqrt-prod_binary64_2481`
38×	`*-un-lft-identity_binary64_2465`
36×	`times-frac_binary64_2471`
26×	`add-cube-cbrt_binary64_2500`
12×	`difference-of-squares_binary64_2434`
11×	`pow1_binary64_2526`
9×	`associate-/r*_binary64_2409`
6×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `distribute-lft-out--_binary64_2417`
4×	`sqrt-pow1_binary64_2483` `sqrt-div_binary64_2482` `associate-/l*_binary64_2410`
3×	`pow-prod-down_binary64_2536` `cancel-sign-sub-inv_binary64_2431`
2×	`pow1/2_binary64_2545` `flip3--_binary64_2469` `flip--_binary64_2440` `associate-/r/_binary64_2411`
1×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `sub-neg_binary64_2458` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `sqrt-undiv_binary64_2486` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462`

Counts

4 → 108

Calls

4 calls:

16.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
10.0ms	(-.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)

series377.0ms (4%)

Error

2.2b

Counts

4 → 43

Calls

4 calls:

122.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
101.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
81.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
31.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 2210 to 1728 computations (21.8% saved)

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4984	4028
1	4984	4028

prune174.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	145	6	151
Fresh	1	6	7
Picked	1	0	1
Done	1	0	1
Total	148	12	160

Error

2.2b

Counts

160 → 12

Compiler

Compiled 4317 to 1704 computations (60.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im))
0.5b	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))
0.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite560.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

2.2b

Rules

402×	`times-frac_binary64_2471`
305×	`add-sqr-sqrt_binary64_2487`
275×	`sqrt-prod_binary64_2481`
252×	`*-un-lft-identity_binary64_2465`
200×	`add-cube-cbrt_binary64_2500`
52×	`difference-of-squares_binary64_2434`
34×	`associate-/r*_binary64_2409`
26×	`distribute-lft-out--_binary64_2417`
15×	`associate-/l*_binary64_2410`
11×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
9×	`div-inv_binary64_2462`
6×	`add-log-exp_binary64_2504`
5×	`pow1_binary64_2526`
4×	`sqrt-div_binary64_2482` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
3×	`cancel-sign-sub-inv_binary64_2431`
2×	`flip3--_binary64_2469` `flip--_binary64_2440` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/l/_binary64_2412`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `flip3-+_binary64_2468` `flip-+_binary64_2439` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `sub-neg_binary64_2458` `associate-/r/_binary64_2411`

Counts

4 → 323

Calls

4 calls:

19.0ms	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))
12.0ms	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 12437 to 3554 computations (71.4% saved)

series466.0ms (4.9%)

Error

0.5b

Counts

4 → 47

Calls

4 calls:

127.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
104.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
101.0ms	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im))
87.0ms	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))

Compiler

Compiled 2503 to 2015 computations (19.5% saved)

simplify183.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4969	15534
1	4969	15534

prune480.0ms (5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	367	3	370
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	375	7	382

Error

0.5b

Counts

382 → 7

Compiler

Compiled 12143 to 3501 computations (71.2% saved)

regimes2.3s (24.2%)

Accuracy

Total 17.3b remaining (97.8%)

Threshold costs 0b (0%)

Compiler

Compiled 19059 to 12812 computations (32.8% saved)

bsearch71.0ms (0.7%)

Steps

Iters	Range		Point
6	6.766582651667305e+77	4.444493611730332e+78	2.6083228972730953e+78
7	-2.209703668501268e-276	-8.625992788711388e-278	-8.72945174690765e-278
8	-8.375240198995856e+71	-1.2128267442629693e+69	-7.802120309188862e+71

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	102
1	59	102

end0.0ms (0%)

sample2.9s (30.3%)

Algorithm

1×

intervals

Results

291.0ms	6125×	body	128	valid
141.0ms	500×	body	4096	valid
136.0ms	596×	body	2048	valid
73.0ms	419×	body	1024	valid
30.0ms	232×	body	512	valid
11.0ms	128×	body	256	valid

Compiler

Compiled 2594 to 1760 computations (32.2% saved)

Details

analyze414.0ms (4.3%)

sample29.0ms (0.3%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite97.0ms (1%)

series341.0ms (3.6%)

simplify52.0ms (0.5%)

prune95.0ms (1%)

localize13.0ms (0.1%)

rewrite86.0ms (0.9%)

series408.0ms (4.3%)

simplify70.0ms (0.7%)

prune120.0ms (1.3%)

localize12.0ms (0.1%)

rewrite177.0ms (1.8%)

series377.0ms (4%)

simplify83.0ms (0.9%)

prune174.0ms (1.8%)

localize13.0ms (0.1%)

rewrite560.0ms (5.9%)

series466.0ms (4.9%)

simplify183.0ms (1.9%)

prune480.0ms (5%)

regimes2.3s (24.2%)

bsearch71.0ms (0.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (30.3%)

Profiling