Details

analyze73.0ms (6.7%)

Algorithm

1×

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
12.5%	87.4%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample17.0ms (1.6%)

Algorithm

1×

intervals

Results

6.0ms	196×	body	80	valid
2.0ms	21×	body	320	valid
2.0ms	14×	body	640	valid
1.0ms	19×	body	160	valid
1.0ms	6×	body	1280	valid

Compiler

Compiled 23 to 23 computations (0% saved)

simplify214.0ms (19.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (201.0ms)

Iter	Nodes	Cost
0	5621	16

prune3.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 20.8b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.6%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 1 x) y)
3.9b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
6.6b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

rewrite27.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`associate-/r_binary64` `difference-of-squares_binary64` `times-frac_binary64` `associate-l/_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

3 → 64

Calls

3 calls:

10.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
8.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
7.0ms	(*.f64 (-.f64 1 x) y)

series23.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
7.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
5.0ms	(*.f64 (-.f64 1 x) y)

simplify70.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5651	1078

prune81.0ms (7.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Merged error: 0.1b

Counts

74 → 3

Compiler

Compiled 1216 to 901 computations (25.9% saved)

localize6.0ms (0.6%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y)))
3.9b	(-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y))))

rewrite21.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
13×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-l_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`flip3--_binary64` `distribute-lft-out_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

2 → 55

Calls

2 calls:

13.0ms	(*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y)))
6.0ms	(-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y))))

series17.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

11.0ms	(-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y))))
7.0ms	(*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y)))

simplify86.0ms (7.9%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5680	1049

prune43.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	61	3	64

Merged error: 0.1b

Counts

64 → 3

Compiler

Compiled 1091 to 786 computations (28% saved)

localize6.0ms (0.5%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (+.f64 x (/.f64 1 y)) (/.f64 x y))
0.0b	(+.f64 x (/.f64 1 y))

rewrite20.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
4×	`distribute-lft-out_binary64`
3×	`distribute-lft-out--_binary64`
2×	`flip3-+_binary64` `pow1_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `div-inv_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `times-frac_binary64` `+-commutative_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

2 → 33

Calls

2 calls:

12.0ms	(-.f64 (+.f64 x (/.f64 1 y)) (/.f64 x y))
6.0ms	(+.f64 x (/.f64 1 y))

series9.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(+.f64 x (/.f64 1 y))
4.0ms	(-.f64 (+.f64 x (/.f64 1 y)) (/.f64 x y))

simplify73.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5044	594

prune27.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	37	5	42

Merged error: 0.1b

Counts

42 → 5

Compiler

Compiled 599 to 356 computations (40.6% saved)

localize12.0ms (1.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 1 (sqrt.f64 (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y)))) (-.f64 1 (sqrt.f64 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y)))))
3.9b	(-.f64 1 (sqrt.f64 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))))
6.6b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
6.6b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))

rewrite54.0ms (5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`
8×	`associate-/r*_binary64` `difference-of-squares_binary64` `times-frac_binary64`
7×	`sqrt-prod_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `flip--_binary64` `associate-*l/_binary64`
5×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

21.0ms	(.f64 (+.f64 1 (sqrt.f64 (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y)))) (-.f64 1 (sqrt.f64 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y)))))
10.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
10.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
9.0ms	(-.f64 1 (sqrt.f64 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))))

series73.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(.f64 (+.f64 1 (sqrt.f64 (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y)))) (-.f64 1 (sqrt.f64 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y)))))
14.0ms	(-.f64 1 (sqrt.f64 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))))
7.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
7.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))

simplify90.0ms (8.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4963	3188
1	4963	3188

Details

analyze73.0ms (6.7%)

sample17.0ms (1.6%)

simplify214.0ms (19.8%)

prune3.0ms (0.3%)

localize7.0ms (0.6%)

rewrite27.0ms (2.5%)

series23.0ms (2.1%)

simplify70.0ms (6.5%)

prune81.0ms (7.5%)

localize6.0ms (0.6%)

rewrite21.0ms (1.9%)

series17.0ms (1.6%)

simplify86.0ms (7.9%)

prune43.0ms (3.9%)

localize6.0ms (0.5%)

rewrite20.0ms (1.8%)

series9.0ms (0.8%)

simplify73.0ms (6.8%)

prune27.0ms (2.5%)

localize12.0ms (1.1%)

rewrite54.0ms (5%)

series73.0ms (6.7%)

simplify90.0ms (8.3%)

prune31.0ms (2.8%)

Profiling