Details

analyze514.0ms (12%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify97.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune3.0ms (0.1%)

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: 24.1b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
23.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`times-frac_binary64_1448`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
3×	`associate-/r_binary64_1386` `associate-/l_binary64_1387` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `pow1_binary64_1503`
1×	`cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `div-exp_binary64_1493`

Counts

2 → 42

Calls

2 calls:

12.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series94.0ms (2.2%)

Counts

2 → 24

Calls

2 calls:

69.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
24.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify53.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5131	2055

prune86.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	5	67

Merged error: 6.0b

Counts

67 → 5

Compiler

Compiled 1574 to 579 computations (63.2% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
14.9b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
28.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.0b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1442`
28×	`sqrt-prod_binary64_1458`
25×	`add-sqr-sqrt_binary64_1464`
24×	`times-frac_binary64_1448`
23×	`add-cube-cbrt_binary64_1477`
10×	`distribute-lft-out_binary64_1393` `unpow-prod-down_binary64_1521`
8×	`associate-/r*_binary64_1386`
6×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `pow1_binary64_1503`
5×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`associate-/l*_binary64_1387`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `pow1/2_binary64_1522`
1×	`cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `div-exp_binary64_1493`

Counts

4 → 94

Calls

4 calls:

16.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series176.0ms (4.1%)

Counts

4 → 36

Calls

4 calls:

97.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
27.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
27.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
25.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4994	3780
1	4994	3780

prune160.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	129	6	135

Merged error: 6.0b

Counts

135 → 6

Compiler

Compiled 4257 to 1729 computations (59.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))
15.0b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
28.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.0b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1442`
28×	`sqrt-prod_binary64_1458`
25×	`add-sqr-sqrt_binary64_1464`
24×	`times-frac_binary64_1448`
23×	`add-cube-cbrt_binary64_1477`
10×	`distribute-lft-out_binary64_1393` `unpow-prod-down_binary64_1521`
8×	`associate-/l*_binary64_1387`
6×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `pow1_binary64_1503`
5×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`associate-/r*_binary64_1386`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `pow1/2_binary64_1522`
1×	`cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `div-exp_binary64_1493`

Counts

4 → 94

Calls

4 calls:

13.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))

series177.0ms (4.2%)

Counts

4 → 36

Calls

4 calls:

101.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
29.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
24.0ms	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))
23.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify95.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4988	3977
1	4988	3977

prune186.0ms (4.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	129	7	136

Merged error: 6.0b

Counts

136 → 7

Compiler

Compiled 4637 to 2110 computations (54.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
14.9b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
28.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite47.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_1442`
30×	`sqrt-prod_binary64_1458`
25×	`add-sqr-sqrt_binary64_1464`
24×	`times-frac_binary64_1448`
23×	`add-cube-cbrt_binary64_1477`
12×	`distribute-lft-out_binary64_1393` `unpow-prod-down_binary64_1521`
8×	`associate-/r*_binary64_1386`
6×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `pow1_binary64_1503`
5×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`associate-/l*_binary64_1387`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `pow1/2_binary64_1522`
1×	`cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `div-exp_binary64_1493`

Counts

4 → 96

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series165.0ms (3.9%)

Counts

4 → 36

Calls

4 calls:

92.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
25.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
23.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4973	3810
1	4973	3810

prune209.0ms (4.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	132	7	139

Merged error: 6.0b

Counts

139 → 7

Compiler

Compiled 4465 to 2613 computations (41.5% saved)

regimes504.0ms (11.8%)

Compiler: Compiled 4233 to 3014 computations (28.8% saved)

bsearch71.0ms (1.7%)

Steps

Iters	Range		Point
7	8.807204181250016e+36	1.4387104667602985e+38	1.210778884969343e+38
5	7.517343559234859e-127	2.6994907770972477e-126	1.2738629973484845e-126
9	-6.937213095154116e-151	-1.4666092893965488e-157	-3.5527736949593474e-151
7	-8.096408219922533e+110	-7.382589490594921e+108	-8.600885342054216e+109

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	190
1	52	190

end0.0ms (0%)

sample1.3s (30%)

Algorithm

1×

intervals

Results

330.0ms	8000×	body	128	valid
19.0ms	478×	body	128	invalid

Compiler

Compiled 956 to 663 computations (30.6% saved)

Details

analyze514.0ms (12%)

sample20.0ms (0.5%)

simplify97.0ms (2.3%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite19.0ms (0.4%)

series94.0ms (2.2%)

simplify53.0ms (1.3%)

prune86.0ms (2%)

localize16.0ms (0.4%)

rewrite40.0ms (0.9%)

series176.0ms (4.1%)

simplify88.0ms (2%)

prune160.0ms (3.8%)

localize18.0ms (0.4%)

rewrite38.0ms (0.9%)

series177.0ms (4.2%)

simplify95.0ms (2.2%)

prune186.0ms (4.4%)

localize13.0ms (0.3%)

rewrite47.0ms (1.1%)

series165.0ms (3.9%)

simplify87.0ms (2%)

prune209.0ms (4.9%)

regimes504.0ms (11.8%)

bsearch71.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (30%)

Profiling