Details

analyze329.0ms (8.2%)

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)

sample32.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	199×	body	128	valid
4.0ms	14×	body	4096	valid
4.0ms	256×	pre	128	true
3.0ms	15×	body	2048	valid
3.0ms	17×	body	1024	valid
1.0ms	8×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify168.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	156	23
1	156	23

prune2.0ms (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: 36.9b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.3%)

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)))
27.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_445`
7×	`*-un-lft-identity_binary64_423` `pow1_binary64_484`
5×	`add-cube-cbrt_binary64_458` `sqrt-prod_binary64_439` `add-log-exp_binary64_462`
4×	`sqrt-div_binary64_440`
3×	`cancel-sign-sub-inv_binary64_389` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `sqrt-pow1_binary64_441`
2×	`flip3--_binary64_427` `associate-*r/_binary64_365` `difference-of-squares_binary64_392` `pow1/2_binary64_503` `flip--_binary64_398`
1×	`pow-prod-down_binary64_494` `sub-neg_binary64_416` `flip-+_binary64_397` `diff-log_binary64_515` `rem-sqrt-square_binary64_436` `distribute-lft-out--_binary64_375` `flip3-+_binary64_426`

Counts

3 → 45

Calls

3 calls:

10.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series327.0ms (8.2%)

Counts

3 → 9

Calls

3 calls:

213.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
60.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
54.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5312	932

prune215.0ms (5.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	46	8	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	8	55

Merged error: 8.2b

Counts

55 → 8

Compiler

Compiled 3894 to 2321 computations (40.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.2b	(sqrt.f64 (*.f64 2 (-.f64 im re)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_484`
2×	`sqrt-div_binary64_440` `associate-*r/_binary64_365` `sqrt-pow1_binary64_441`
1×	`*-un-lft-identity_binary64_423` `pow-prod-down_binary64_494` `add-cube-cbrt_binary64_458` `sqrt-prod_binary64_439` `add-sqr-sqrt_binary64_445` `flip3--_binary64_427` `add-exp-log_binary64_461` `pow1/2_binary64_503` `add-cbrt-cube_binary64_459` `add-log-exp_binary64_462` `flip--_binary64_398`

Counts

1 → 13

Calls

1 calls:

5.0ms

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

series110.0ms (2.7%)

Counts

1 → 3

Calls

1 calls:

109.0ms

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

simplify53.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5019	253

prune29.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	15	9	24

Merged error: 8.1b

Counts

24 → 9

Compiler

Compiled 519 to 351 computations (32.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_445`
17×	`sqrt-prod_binary64_439`
11×	`*-un-lft-identity_binary64_423`
8×	`associate-r_binary64_363`
7×	`add-cube-cbrt_binary64_458` `pow1_binary64_484`
6×	`associate-l_binary64_364`
4×	`sqrt-div_binary64_440` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `unswap-sqr_binary64_391`
3×	`pow-prod-down_binary64_494` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`
2×	`flip3--_binary64_427` `associate-*r/_binary64_365` `distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392` `add-log-exp_binary64_462` `flip--_binary64_398`
1×	`prod-exp_binary64_472` `rem-sqrt-square_binary64_436` `*-commutative_binary64_354` `sqrt-unprod_binary64_443` `cbrt-unprod_binary64_456`

Counts

2 → 51

Calls

2 calls:

11.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series172.0ms (4.3%)

Counts

2 → 6

Calls

2 calls:

114.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
58.0ms	(sqrt.f64 (-.f64 im re))

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4962	838
1	4962	838

prune86.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	57	9	66

Merged error: 8.1b

Counts

66 → 9

Compiler

Compiled 1508 to 961 computations (36.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (sqrt.f64 (-.f64 im re)))
0.0b	(sqrt.f64 (-.f64 im re))
0.4b	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
3.8b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_445`
28×	`sqrt-prod_binary64_439` `log-prod_binary64_509`
23×	`*-un-lft-identity_binary64_423`
20×	`exp-sum_binary64_469`
15×	`add-cube-cbrt_binary64_458`
11×	`pow1_binary64_484` `associate-r_binary64_363`
8×	`sqrt-div_binary64_440`
6×	`associate-l_binary64_364` `log-pow_binary64_512` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `log-div_binary64_510` `unswap-sqr_binary64_391` `exp-prod_binary64_475`
4×	`exp-diff_binary64_471` `flip3--_binary64_427` `distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392` `add-log-exp_binary64_462` `flip--_binary64_398`
3×	`pow1/2_binary64_503` `sqrt-pow1_binary64_441`
2×	`associate-*r/_binary64_365`
1×	`pow-prod-down_binary64_494` `prod-exp_binary64_472` `rem-sqrt-square_binary64_436` `rem-exp-log_binary64_463` `*-commutative_binary64_354` `rem-log-exp_binary64_464` `cbrt-unprod_binary64_456`

Counts

4 → 98

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
7.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
5.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series658.0ms (16.4%)

Counts

4 → 12

Calls

4 calls:

315.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
218.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
70.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
55.0ms	(sqrt.f64 (-.f64 im re))

simplify56.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5125	1612

prune111.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	110	9	119

Merged error: 8.1b

Counts

119 → 9

Compiler

Compiled 2156 to 1248 computations (42.1% saved)

regimes137.0ms (3.4%)

Compiler: Compiled 613 to 419 computations (31.6% saved)

bsearch73.0ms (1.8%)

Steps

Iters	Range	Point
8	3.644294487492142e-19	5.9826746879980365e-15	3.703600935120756e-19
9	-2.7260457505491215e-65	-6.681870966069836e-71	-6.747633475511543e-71
8	-1.8773592324894852e+122	-5.264206973461443e+119	-5.523275979831376e+120

Iters

Range

Point

3.644294487492142e-19

5.9826746879980365e-15

3.703600935120756e-19

-2.7260457505491215e-65

-6.681870966069836e-71

-6.747633475511543e-71

-1.8773592324894852e+122

-5.264206973461443e+119

-5.523275979831376e+120

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	63	114
1	63	114

end0.0ms (0%)

sample1.2s (29.7%)

Algorithm

1×

intervals

Results

281.0ms	6064×	body	128	valid
151.0ms	504×	body	4096	valid
143.0ms	631×	body	2048	valid
117.0ms	8000×	pre	128	true
77.0ms	440×	body	1024	valid
32.0ms	249×	body	512	valid
10.0ms	112×	body	256	valid

Compiler

Compiled 248 to 165 computations (33.5% saved)

Details

analyze329.0ms (8.2%)

sample32.0ms (0.8%)

simplify168.0ms (4.2%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

rewrite31.0ms (0.8%)

series327.0ms (8.2%)

simplify59.0ms (1.5%)

prune215.0ms (5.4%)

localize6.0ms (0.1%)

rewrite6.0ms (0.1%)

series110.0ms (2.7%)

simplify53.0ms (1.3%)

prune29.0ms (0.7%)

localize7.0ms (0.2%)

rewrite18.0ms (0.5%)

series172.0ms (4.3%)

simplify70.0ms (1.7%)

prune86.0ms (2.1%)

localize10.0ms (0.3%)

rewrite39.0ms (1%)

series658.0ms (16.4%)

simplify56.0ms (1.4%)

prune111.0ms (2.8%)

regimes137.0ms (3.4%)

bsearch73.0ms (1.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (29.7%)

Profiling