Details

analyze125.0ms (4.2%)

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
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample15.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify25.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
148×	`fma-neg_binary64`
84×	`distribute-rgt-in_binary64`
50×	`distribute-lft-in_binary64`
50×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

series7.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
16×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

1 → 51

Calls

1 calls:

7.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

simplify113.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-neg_binary64`
433×	`exp-prod_binary64`
400×	`*-commutative_binary64`
343×	`fma-def_binary64`
288×	`associate-+r+_binary64`

Counts

75 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1085
1	223	985
2	948	871
3	2323	814
4	4186	814
5	4991	814
6	4915	814
7	4901	814

prune49.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Error

0.0b

Counts

74 → 5

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	12.4b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	33.2b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
▶	1.1b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))))
	4.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 1420 to 610 computations (57% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (*.f64 x y) (-.f64 1 y))))
✓	9.9b	(cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))

series969.0ms (32.2%)

Counts

3 → 72

Calls

3 calls:

595.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y))) (cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y))))

338.0ms

(cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y)))

36.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y))) (cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y)))) (cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y))))

rewrite37.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

10.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y))) (cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y)))) (cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y))))

5.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y))) (cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y))))

4.0ms

(cbrt.f64 (*.f64 (*.f64 x y) (-.f64 1 y)))

simplify170.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-def_binary64`
601×	`times-frac_binary64`
297×	`cancel-sign-sub-inv_binary64`
296×	`fma-neg_binary64`
231×	`associate-l_binary64`

Counts

187 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	288	5751
1	693	5324
2	2213	4690
3	4848	4688
4	4959	4688

prune415.0ms (13.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	553	0	553
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	553	5	558

Error

0.0b

Counts

558 → 5

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	12.4b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	33.2b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
✓	1.1b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))))
▶	4.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 21014 to 11610 computations (44.8% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.1b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

series13.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

13.0ms

(*.f64 (-.f64 y (pow.f64 y 2)) x)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`associate-l_binary64`
6×	`*-un-lft-identity_binary64`
4×	`difference-of-squares_binary64`
3×	`associate-r_binary64`

Counts

1 → 28

Calls

1 calls:

6.0ms

(*.f64 (-.f64 y (pow.f64 y 2)) x)

simplify62.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

844×	`fma-def_binary64`
363×	`associate-l_binary64`
306×	`neg-sub0_binary64`
294×	`associate-r_binary64`
293×	`neg-mul-1_binary64`

Counts

40 → 51

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	512
1	146	450
2	438	447
3	1674	447
4	4020	447
5	5027	447

prune32.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	51	5	56

Error

0.0b

Counts

56 → 5

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
▶	12.4b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	33.2b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
✓	1.1b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))))
✓	4.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 800 to 407 computations (49.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 y))
✓	0.0b	(.f64 (.f64 x y) (sqrt.f64 (-.f64 1 y)))
✓	0.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))

series37.0ms (1.2%)

Counts

3 → 44

Calls

3 calls:

18.0ms	(.f64 (.f64 x y) (sqrt.f64 (-.f64 1 y)))
11.0ms	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
7.0ms	(sqrt.f64 (-.f64 1 y))

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`sqrt-prod_binary64`
18×	`associate-r_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`pow1_binary64`
17×	`*-un-lft-identity_binary64`

Counts

3 → 85

Calls

3 calls:

12.0ms	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
7.0ms	(.f64 (.f64 x y) (sqrt.f64 (-.f64 1 y)))
5.0ms	(sqrt.f64 (-.f64 1 y))

simplify98.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

524×	`*-commutative_binary64`
460×	`fma-def_binary64`
361×	`associate-l_binary64`
333×	`fma-neg_binary64`
321×	`cancel-sign-sub-inv_binary64`

Counts

129 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1853
1	373	1689
2	1352	1668
3	2949	1656
4	4698	1656
5	4966	1656

prune117.0ms (3.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	166	5	171

Error

0.0b

Counts

171 → 5

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
✓	12.4b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	33.2b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
✓	1.1b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))))
✓	4.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 3341 to 2169 computations (35.1% saved)

regimes105.0ms (3.5%)

Accuracy

Total 0.1b remaining (78.2%)

Threshold costs 0.1b (78.2%)

Counts

35 → 1

Compiler

Compiled 1938 to 1337 computations (31% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	17	10
3	19	10
4	20	10
5	19	10

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample549.0ms (18.2%)

Algorithm

1×

intervals

Results

222.0ms	8000×	body	128	valid
5.0ms	176×	body	128	invalid

Compiler

Compiled 96 to 65 computations (32.3% saved)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Details

analyze125.0ms (4.2%)

sample15.0ms (0.5%)

simplify25.0ms (0.8%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite10.0ms (0.3%)

simplify113.0ms (3.8%)

prune49.0ms (1.6%)

localize7.0ms (0.2%)

series969.0ms (32.2%)

rewrite37.0ms (1.2%)

simplify170.0ms (5.6%)

prune415.0ms (13.8%)

localize4.0ms (0.1%)

series13.0ms (0.4%)

rewrite8.0ms (0.3%)

simplify62.0ms (2.1%)

prune32.0ms (1%)

localize6.0ms (0.2%)

series37.0ms (1.2%)

rewrite29.0ms (1%)

simplify98.0ms (3.3%)

prune117.0ms (3.9%)

regimes105.0ms (3.5%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample549.0ms (18.2%)

Profiling

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10