Details

analyze326.0ms (7.1%)

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)

sample28.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	207×	body	128	valid
5.0ms	16×	body	4096	valid
3.0ms	11×	body	2048	valid
2.0ms	11×	body	1024	valid
1.0ms	8×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify93.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0.1%)

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: 36.3b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize15.0ms (0.3%)

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))
0.6b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 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)
5.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series183.0ms (4%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
27.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
19.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4937	1040
1	4937	1040

prune77.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	7	64

Merged error: 13.6b

Counts

64 → 7

Compiler

Compiled 1349 to 618 computations (54.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

7.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

23.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series102.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4979	928
1	4979	928

prune85.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Merged error: 13.6b

Counts

75 → 7

Compiler

Compiled 2563 to 736 computations (71.3% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

12.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

23.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series199.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
28.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify110.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4916	946
1	4916	946

prune89.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	67	8	75

Merged error: 13.6b

Counts

75 → 8

Compiler

Compiled 2669 to 782 computations (70.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (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)
28.3b	(sqrt.f64 (.f64 (.f64 im im) 2))
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite42.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

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` `distribute-lft-out--_binary64_2417` `add-cbrt-cube_binary64_2501`
4×	`sqrt-div_binary64_2482` `sqrt-pow1_binary64_2483` `associate-/l*_binary64_2410`
3×	`cancel-sign-sub-inv_binary64_2431` `pow-prod-down_binary64_2536`
2×	`flip--_binary64_2440` `pow1/2_binary64_2545` `associate-/r/_binary64_2411` `flip3--_binary64_2469`
1×	`flip3-+_binary64_2468` `sqrt-undiv_binary64_2486` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `frac-2neg_binary64_2476`

Counts

4 → 108

Calls

4 calls:

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

series166.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
31.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5054	3621

prune136.0ms (3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

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

Merged error: 8.2b

Counts

128 → 10

Compiler

Compiled 3518 to 1216 computations (65.4% saved)

regimes910.0ms (19.9%)

Compiler: Compiled 5258 to 3598 computations (31.6% saved)

bsearch83.0ms (1.8%)

Steps

Iters	Range	Point
10	1.105764718465146e+139	1.623268606663559e+150	4.943285085157152e+144
7	5.855532259510251e-298	3.000886600218849e-296	5.940568352251136e-298
8	-2.9143576829745053e+192	-6.1438198913427996e+187	-6.2492827667685015e+187

Iters

Range

Point

1.105764718465146e+139

1.623268606663559e+150

4.943285085157152e+144

5.855532259510251e-298

3.000886600218849e-296

5.940568352251136e-298

-2.9143576829745053e+192

-6.1438198913427996e+187

-6.2492827667685015e+187

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%)

sample1.5s (33.5%)

Algorithm

1×

intervals

Results

301.0ms	6106×	body	128	valid
155.0ms	648×	body	2048	valid
142.0ms	486×	body	4096	valid
85.0ms	416×	body	1024	valid
31.0ms	231×	body	512	valid
10.0ms	113×	body	256	valid

Compiler

Compiled 762 to 513 computations (32.7% saved)

Details

analyze326.0ms (7.1%)

sample28.0ms (0.6%)

simplify93.0ms (2%)

prune3.0ms (0.1%)

localize15.0ms (0.3%)

rewrite28.0ms (0.6%)

series183.0ms (4%)

simplify79.0ms (1.7%)

prune77.0ms (1.7%)

localize15.0ms (0.3%)

rewrite45.0ms (1%)

series102.0ms (2.2%)

simplify71.0ms (1.6%)

prune85.0ms (1.9%)

localize21.0ms (0.4%)

rewrite44.0ms (1%)

series199.0ms (4.4%)

simplify110.0ms (2.4%)

prune89.0ms (1.9%)

localize13.0ms (0.3%)

rewrite42.0ms (0.9%)

series166.0ms (3.6%)

simplify71.0ms (1.6%)

prune136.0ms (3%)

regimes910.0ms (19.9%)

bsearch83.0ms (1.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (33.5%)

Profiling