Details

analyze331.0ms (2.2%)

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)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	190×	body	80	valid
7.0ms	27×	body	2560	valid
6.0ms	9×	body	5120	valid
4.0ms	256×	pre	80	true
3.0ms	13×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	157	23
1	157	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

Merged error: 40.6b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize11.0ms (0.1%)

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))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`sqrt-pow1_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 57

Calls

4 calls:

11.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(+.f64 (.f64 re re) (.f64 im im))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series340.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(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)
47.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
38.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5177	1181

prune93.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	6	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 9.2b

Counts

70 → 6

Compiler

Compiled 1441 to 647 computations (55.1% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `insert-posit16` `flip--_binary64` `sqrt-prod_binary64`

Counts

1 → 14

Calls

1 calls:

6.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

series104.0ms (0.7%)

Counts

1 → 3

Calls

1 calls:

104.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4968	264
1	4968	264

prune20.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	16	7	23

Merged error: 9.2b

Counts

23 → 7

Compiler

Compiled 323 to 230 computations (28.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
0.0b	(sqrt.f64 (*.f64 2 (-.f64 im re)))
3.6b	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
8×	`log-prod_binary64` `log-pow_binary64`
7×	`exp-prod_binary64`
6×	`-un-lft-identity_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64` `add-sqr-sqrt_binary64` `sqrt-div_binary64`
4×	`add-exp-log_binary64` `exp-sum_binary64` `log-div_binary64`
3×	`pow-prod-down_binary64` `add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip--_binary64` `sqrt-prod_binary64`
2×	`exp-diff_binary64`
1×	`rem-log-exp_binary64` `rem-exp-log_binary64`

Counts

3 → 55

Calls

3 calls:

11.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
7.0ms	(log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
6.0ms	(sqrt.f64 (*.f64 2 (-.f64 im re)))

series342.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

121.0ms	(log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
114.0ms	(sqrt.f64 (*.f64 2 (-.f64 im re)))
107.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))

simplify125.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4944	1016
1	4944	1016

prune70.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	64	7	71

Merged error: 9.2b

Counts

71 → 7

Compiler

Compiled 1109 to 779 computations (29.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
0.4b	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
2.0b	(exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))))
3.5b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`cbrt-prod_binary64`
17×	`pow1_binary64`
12×	`log-pow_binary64`
10×	`pow-unpow_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`
6×	`sqrt-pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `pow-pow_binary64` `unpow-prod-down_binary64`
2×	`pow1/3_binary64` `exp-to-pow_binary64` `exp-prod_binary64`
1×	`pow-to-exp_binary64` `sqr-pow_binary64` `rem-exp-log_binary64` `pow-exp_binary64`

Counts

4 → 70

Calls

4 calls:

9.0ms	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))
6.0ms	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
6.0ms	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
2.0ms	(exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))))

series11.3s (75.6%)

Counts

4 → 12

Calls

4 calls:

3.5s	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
3.4s	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
3.0s	(exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))))
1.2s	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))

simplify128.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5002	6587

prune319.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	82	7	89

Merged error: 9.2b

Counts

89 → 7

Compiler

Compiled 5289 to 3894 computations (26.4% saved)

regimes111.0ms (0.7%)

Compiler: Compiled 459 to 379 computations (17.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	50	73
1	50	73

end0.0ms (0%)

sample1.3s (8.5%)

Algorithm

1×

intervals

Results

301.0ms	6024×	body	80	valid
198.0ms	711×	body	2560	valid
116.0ms	8000×	pre	80	true
110.0ms	487×	body	1280	valid
91.0ms	273×	body	5120	valid
47.0ms	268×	body	640	valid
20.0ms	155×	body	320	valid
7.0ms	82×	body	160	valid

Compiler

Compiled 191 to 150 computations (21.5% saved)

Details

analyze331.0ms (2.2%)

sample40.0ms (0.3%)

simplify31.0ms (0.2%)

prune3.0ms (0%)

localize11.0ms (0.1%)

rewrite33.0ms (0.2%)

series340.0ms (2.3%)

simplify71.0ms (0.5%)

prune93.0ms (0.6%)

localize6.0ms (0%)

rewrite6.0ms (0%)

series104.0ms (0.7%)

simplify98.0ms (0.7%)

prune20.0ms (0.1%)

localize9.0ms (0.1%)

rewrite26.0ms (0.2%)

series342.0ms (2.3%)

simplify125.0ms (0.8%)

prune70.0ms (0.5%)

localize17.0ms (0.1%)

rewrite26.0ms (0.2%)

series11.3s (75.6%)

simplify128.0ms (0.9%)

prune319.0ms (2.1%)

regimes111.0ms (0.7%)

bsearch2.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample1.3s (8.5%)

Profiling