Details

analyze359.0ms (8.5%)

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)

sample36.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	194×	body	128	valid
5.0ms	17×	body	4096	valid
5.0ms	21×	body	2048	valid
4.0ms	256×	pre	128	true
2.0ms	10×	body	1024	valid
1.0ms	9×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify167.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	156	23
1	156	23

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: 39.6b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_445`
8×	`*-un-lft-identity_binary64_423` `pow1_binary64_484` `add-log-exp_binary64_462`
6×	`add-cube-cbrt_binary64_458`
5×	`sqrt-prod_binary64_439`
4×	`sqrt-div_binary64_440` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
3×	`cancel-sign-sub-inv_binary64_389` `sqrt-pow1_binary64_441`
2×	`flip-+_binary64_397` `flip3--_binary64_427` `associate-*r/_binary64_365` `flip3-+_binary64_426` `difference-of-squares_binary64_392` `pow1/2_binary64_503` `flip--_binary64_398`
1×	`pow-prod-down_binary64_494` `sub-neg_binary64_416` `diff-log_binary64_515` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `distribute-lft-out--_binary64_375` `sum-log_binary64_514`

Counts

4 → 56

Calls

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

series352.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(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)
48.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
39.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5363	1125

prune255.0ms (6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 10.7b

Counts

69 → 7

Compiler

Compiled 4389 to 2654 computations (39.5% 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)))

series109.0ms (2.6%)

Counts

1 → 3

Calls

1 calls:

109.0ms

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

simplify51.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5019	253

prune38.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	14	9	23

Merged error: 10.4b

Counts

23 → 9

Compiler

Compiled 548 to 425 computations (22.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

rewrite19.0ms (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:

12.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series162.0ms (3.8%)

Counts

2 → 6

Calls

2 calls:

102.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
60.0ms	(sqrt.f64 (-.f64 im re))

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4962	838
1	4962	838

prune54.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

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

Merged error: 10.4b

Counts

66 → 9

Compiler

Compiled 964 to 592 computations (38.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
0.2b	(sqrt.f64 (*.f64 2 (-.f64 im re)))
3.5b	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64_484`
8×	`log-pow_binary64_512` `log-prod_binary64_509`
7×	`exp-prod_binary64_475`
6×	`-un-lft-identity_binary64_423` `sqrt-div_binary64_440` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445` `associate-r/_binary64_365` `sqrt-pow1_binary64_441`
4×	`exp-sum_binary64_469` `add-exp-log_binary64_461` `log-div_binary64_510`
3×	`pow-prod-down_binary64_494` `sqrt-prod_binary64_439` `flip3--_binary64_427` `pow1/2_binary64_503` `add-cbrt-cube_binary64_459` `add-log-exp_binary64_462` `flip--_binary64_398`
2×	`exp-diff_binary64_471`
1×	`rem-exp-log_binary64_463` `rem-log-exp_binary64_464`

Counts

3 → 52

Calls

3 calls:

8.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
6.0ms	(log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
5.0ms	(sqrt.f64 (*.f64 2 (-.f64 im re)))

series534.0ms (12.6%)

Counts

3 → 9

Calls

3 calls:

323.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
107.0ms	(log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
103.0ms	(sqrt.f64 (*.f64 2 (-.f64 im re)))

simplify114.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4960	988
1	4960	988

prune67.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	61	9	70

Merged error: 10.4b

Counts

70 → 9

Compiler

Compiled 1101 to 789 computations (28.3% saved)

regimes220.0ms (5.2%)

Compiler: Compiled 602 to 518 computations (14% saved)

bsearch154.0ms (3.7%)

Steps

Iters	Range		Point
7	2.5970358639780672e+222	3.150553466321319e+224	2.6360421142108628e+222
7	1.042661322630328e+104	2.1222593530629238e+105	2.1025679527940389e+105
2	1.913795281151403e+20	2.2672195217618004e+20	1.9579733112277025e+20
9	-9.551582641383086e-32	-2.9994944077698054e-40	-3.050262596495973e-40
8	-1.378767339504633e-14	-1.3200675653413458e-18	-4.394426049509313e-15
6	-22738.26765107916	-3990.507752188212	-4029.537249877249
8	-1.2682168657103938e+82	-2.8583380436132328e+79	-5.92404308041133e+81

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	174
1	79	174

end0.0ms (0%)

sample1.3s (30.8%)

Algorithm

1×

intervals

Results

319.0ms	6111×	body	128	valid
163.0ms	534×	body	4096	valid
160.0ms	632×	body	2048	valid
120.0ms	8000×	pre	128	true
77.0ms	385×	body	1024	valid
33.0ms	233×	body	512	valid
10.0ms	105×	body	256	valid

Compiler

Compiled 243 to 184 computations (24.3% saved)

Details

analyze359.0ms (8.5%)

sample36.0ms (0.9%)

simplify167.0ms (3.9%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

rewrite33.0ms (0.8%)

series352.0ms (8.3%)

simplify63.0ms (1.5%)

prune255.0ms (6%)

localize6.0ms (0.1%)

rewrite6.0ms (0.1%)

series109.0ms (2.6%)

simplify51.0ms (1.2%)

prune38.0ms (0.9%)

localize8.0ms (0.2%)

rewrite19.0ms (0.5%)

series162.0ms (3.8%)

simplify68.0ms (1.6%)

prune54.0ms (1.3%)

localize10.0ms (0.2%)

rewrite23.0ms (0.5%)

series534.0ms (12.6%)

simplify114.0ms (2.7%)

prune67.0ms (1.6%)

regimes220.0ms (5.2%)

bsearch154.0ms (3.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (30.8%)

Profiling