Details

analyze177.0ms (5.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	7	20
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Symmetry

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

3×	`add-log-exp_binary64_3527`
1×	`sum-log_binary64_3579` `pow1_binary64_3549` `add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524` `add-cube-cbrt_binary64_3523` `add-sqr-sqrt_binary64_3510` `flip3-+_binary64_3491` `*-un-lft-identity_binary64_3488` `flip-+_binary64_3462` `+-commutative_binary64_3418`

Counts

1 → 11

Calls

1 calls:

4.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

Compiler

Compiled 178 to 40 computations (77.5% saved)

series99.0ms (3.2%)

Error

0.0b

Counts

1 → 12

Calls

1 calls:

90.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

Compiler

Compiled 162 to 152 computations (6.2% saved)

simplify79.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4921	247
1	4921	247

prune16.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	2	24

Error

0.0b

Counts

24 → 2

Compiler

Compiled 235 to 60 computations (74.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 y y) (.f64 x x))
0.0b	(+.f64 (.f64 y y) (.f64 x x))
5.1b	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
5.1b	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))

rewrite61.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

8×	`add-log-exp_binary64_3527` `add-sqr-sqrt_binary64_3510`
6×	`pow1_binary64_3549` `add-cube-cbrt_binary64_3523` `sqrt-prod_binary64_3504` `*-un-lft-identity_binary64_3488`
4×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524` `flip3-+_binary64_3491` `sqrt-div_binary64_3505` `flip-+_binary64_3462`
2×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501` `sum-log_binary64_3579` `+-commutative_binary64_3418`

Counts

4 → 52

Calls

4 calls:

4.0ms	(+.f64 (.f64 y y) (.f64 x x))
4.0ms	(+.f64 (.f64 y y) (.f64 x x))
4.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))

Compiler

Compiled 1374 to 173 computations (87.4% saved)

series382.0ms (12.3%)

Error

Counts

4 → 52

Calls

4 calls:

97.0ms	(+.f64 (.f64 y y) (.f64 x x))
94.0ms	(+.f64 (.f64 y y) (.f64 x x))
79.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
73.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))

Compiler

Compiled 2226 to 1364 computations (38.7% saved)

simplify69.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5029	1422

prune79.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	3	106

Error

Counts

106 → 3

Compiler

Compiled 2171 to 439 computations (79.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 y y) (.f64 x x))
0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x x))) (+.f64 y (.f64 1/2 (/.f64 (*.f64 x x) y))))
5.1b	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
5.5b	(/.f64 (*.f64 x x) y)

rewrite107.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`add-sqr-sqrt_binary64_3510`
11×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
10×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
8×	`flip3-+_binary64_3491` `sqrt-div_binary64_3505` `flip-+_binary64_3462`
7×	`pow1_binary64_3549` `sqrt-prod_binary64_3504`
6×	`add-log-exp_binary64_3527` `associate-l_binary64_3429`
4×	`frac-times_binary64_3498`
3×	`times-frac_binary64_3494` `associate-/r_binary64_3432` `associate-r*_binary64_3428`
2×	`prod-exp_binary64_3537` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `cbrt-unprod_binary64_3521` `unswap-sqr_binary64_3456` `associate-l/_binary64_3431` `associate-r/_binary64_3430`
1×	`frac-2neg_binary64_3499` `clear-num_binary64_3487` `div-inv_binary64_3485` `associate-/l_binary64_3433` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501` `pow-prod-down_binary64_3559` `distribute-rgt-in_binary64_3438` `distribute-lft-in_binary64_3437` `-commutative_binary64_3419` `sum-log_binary64_3579` `+-commutative_binary64_3418`

Counts

4 → 79

Calls

4 calls:

11.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x x))) (+.f64 y (.f64 1/2 (/.f64 (*.f64 x x) y))))
5.0ms	(/.f64 (*.f64 x x) y)
4.0ms	(+.f64 (.f64 y y) (.f64 x x))
4.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))

Compiler

Compiled 2398 to 655 computations (72.7% saved)

series356.0ms (11.5%)

Error

Counts

4 → 39

Calls

4 calls:

107.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x x))) (+.f64 y (.f64 1/2 (/.f64 (*.f64 x x) y))))
86.0ms	(+.f64 (.f64 y y) (.f64 x x))
72.0ms	(/.f64 (*.f64 x x) y)
65.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))

Compiler

Compiled 1582 to 1099 computations (30.5% saved)

simplify70.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4982	2145
1	4982	2145

prune102.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	118	3	121

Error

Counts

121 → 3

Compiler

Compiled 2698 to 876 computations (67.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 y y) (.f64 x x))
0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x x))) (-.f64 (.f64 (/.f64 (*.f64 y y) x) -1/2) x))
5.1b	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
7.4b	(/.f64 (*.f64 y y) x)

rewrite122.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

17×	`add-sqr-sqrt_binary64_3510`
12×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
11×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
8×	`sqrt-div_binary64_3505`
7×	`pow1_binary64_3549` `sqrt-prod_binary64_3504`
6×	`add-log-exp_binary64_3527` `cancel-sign-sub-inv_binary64_3454` `associate-l_binary64_3429`
5×	`flip3-+_binary64_3491` `flip-+_binary64_3462`
4×	`frac-times_binary64_3498` `distribute-rgt-in_binary64_3438` `distribute-lft-in_binary64_3437`
3×	`times-frac_binary64_3494` `associate-/r_binary64_3432` `flip3--_binary64_3492` `flip--_binary64_3463` `associate-r*_binary64_3428`
2×	`prod-exp_binary64_3537` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `cbrt-unprod_binary64_3521` `unswap-sqr_binary64_3456` `sub-neg_binary64_3481` `associate-l/_binary64_3431` `associate-r/_binary64_3430`
1×	`frac-2neg_binary64_3499` `clear-num_binary64_3487` `div-inv_binary64_3485` `associate-/l_binary64_3433` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501` `pow-prod-down_binary64_3559` `-commutative_binary64_3419` `sum-log_binary64_3579` `+-commutative_binary64_3418`

Counts

4 → 85

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x x))) (-.f64 (.f64 (/.f64 (*.f64 y y) x) -1/2) x))
5.0ms	(/.f64 (*.f64 y y) x)
4.0ms	(+.f64 (.f64 y y) (.f64 x x))
4.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))

Compiler

Compiled 2594 to 695 computations (73.2% saved)

series355.0ms (11.4%)

Error

Counts

4 → 35

Calls

4 calls:

115.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x x))) (-.f64 (.f64 (/.f64 (*.f64 y y) x) -1/2) x))
100.0ms	(+.f64 (.f64 y y) (.f64 x x))
72.0ms	(/.f64 (*.f64 y y) x)
44.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))

Compiler

Compiled 1383 to 960 computations (30.6% saved)

simplify73.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4978	2318
1	4978	2318

prune97.0ms (3.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	120	3	123

Error

Counts

123 → 3

Compiler

Compiled 2752 to 835 computations (69.7% saved)

regimes144.0ms (4.7%)

Accuracy

Total 0.0b remaining (83.7%)

Threshold costs 0.0b (83.7%)

Compiler

Compiled 1489 to 810 computations (45.6% saved)

bsearch0.0ms (0%)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	26
1	9	26

Remove

(sort x y)

Compiler

Compiled 34 to 14 computations (58.8% saved)

end0.0ms (0%)

sample621.0ms (20.1%)

Algorithm

1×

intervals

Results

169.0ms

8000×

body

128

valid

Compiler

Compiled 304 to 165 computations (45.7% saved)

Details

analyze177.0ms (5.7%)

sample19.0ms (0.6%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite14.0ms (0.4%)

series99.0ms (3.2%)

simplify79.0ms (2.6%)

prune16.0ms (0.5%)

localize7.0ms (0.2%)

rewrite61.0ms (2%)

series382.0ms (12.3%)

simplify69.0ms (2.2%)

prune79.0ms (2.6%)

localize11.0ms (0.3%)

rewrite107.0ms (3.4%)

series356.0ms (11.5%)

simplify70.0ms (2.3%)

prune102.0ms (3.3%)

localize10.0ms (0.3%)

rewrite122.0ms (3.9%)

series355.0ms (11.4%)

simplify73.0ms (2.4%)

prune97.0ms (3.1%)

regimes144.0ms (4.7%)

bsearch0.0ms (0%)

simplify10.0ms (0.3%)

end0.0ms (0%)

sample621.0ms (20.1%)

Profiling