Details

analyze77.0ms (0.8%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
25%	37.5%	37.6%	6
31.2%	31.2%	37.6%	7
37.5%	18.7%	43.8%	8
39%	15.6%	45.4%	9
42.1%	9.4%	48.5%	10
42.9%	7.8%	49.3%	11
44.5%	4.7%	50.8%	12
44.9%	3.9%	51.2%	13
45.7%	2.3%	52%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample952.0ms (9.8%)

Results

793.0ms	8252×	body	128	valid
18.0ms	197×	body	128	invalid
1.0ms	4×	body	1024	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Rules

151×	`fma-def_binary64`
131×	`fma-neg_binary64`
45×	`cancel-sign-sub-inv_binary64`
38×	`sub-neg_binary64`
31×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 35 to 22 computations (37.1% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

Counts

1 → 15

Calls

1 calls:

7.0ms

(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

709×	`distribute-rgt-in_binary64`
693×	`distribute-lft-in_binary64`
571×	`neg-mul-1_binary64`
544×	`unsub-neg_binary64`
296×	`associate-+l+_binary64`

Counts

25 → 25

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	263
1	34	241
2	94	241
3	413	241
4	2431	241
5	4317	241
6	4957	241

prune53.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	3	26

Error

0.1b

Counts

26 → 3

Alt Table

Status	Error	Program
	34.8b	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
▶	31.6b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

Compiler

Compiled 326 to 182 computations (44.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3)
✓	0.1b	(fma.f64 y (sqrt.f64 x) 1)
✓	29.6b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3))

series63.0ms (0.6%)

Counts

3 → 43

Calls

3 calls:

45.0ms	(pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3)
9.0ms	(fma.f64 y (sqrt.f64 x) 1)
8.0ms	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
10×	`cube-prod_binary64`
10×	`unpow-prod-down_binary64`

Counts

3 → 70

Calls

3 calls:

3.0ms	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3))
3.0ms	(pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3)
0.0ms	(fma.f64 y (sqrt.f64 x) 1)

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
623×	`distribute-rgt-in_binary64`
604×	`distribute-lft-in_binary64`
207×	`unswap-sqr_binary64`
175×	`cancel-sign-sub-inv_binary64`

Counts

113 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	2170
1	369	2024
2	1298	1893
3	5069	1893

prune122.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	101	5	106

Error

0.0b

Counts

106 → 5

Alt Table

Status	Error	Program
	25.2b	(.f64 (cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x))) 3)) (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) 3)))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	34.8b	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	34.1b	(cbrt.f64 (+.f64 (fma.f64 3 (.f64 y (+.f64 (sqrt.f64 x) (.f64 x y))) (fma.f64 3 (fma.f64 x x (.f64 y (pow.f64 x 5/2))) (.f64 (pow.f64 x 3/2) (pow.f64 y 3)))) (-.f64 1 (fma.f64 (.f64 x x) (+.f64 x (.f64 3 (.f64 y y))) (fma.f64 x 3 (.f64 6 (*.f64 y (pow.f64 x 3/2))))))))
▶	25.0b	(*.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2)) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)))

Compiler

Compiled 2256 to 1414 computations (37.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 x) 1)
✓	0.2b	(*.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2)) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)))
✓	0.4b	(cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x))
✓	23.8b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2))

series199.0ms (2%)

Counts

3 → 45

Calls

3 calls:

117.0ms

(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2))

72.0ms

(cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x))

10.0ms

(*.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2)) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`cbrt-prod_binary64`
35×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
13×	`associate-l_binary64`
12×	`unpow-prod-down_binary64`

Counts

3 → 86

Calls

3 calls:

11.0ms

(*.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2)) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)))

3.0ms

(cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x))

3.0ms

(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2))

simplify133.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

530×	`times-frac_binary64`
350×	`fma-def_binary64`
279×	`associate-r_binary64`
263×	`*-commutative_binary64`
223×	`fma-neg_binary64`

Counts

131 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	405	5808
1	1179	5411
2	4158	5305
3	5038	5305

prune229.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	188	3	191
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	190	6	196

Error

0.0b

Counts

196 → 6

Alt Table

Status	Error	Program
	25.0b	(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2))) (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2))) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x))))
	34.8b	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
▶	0.9b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) 3)
	25.1b	(.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2)) (/.f64 (cbrt.f64 (-.f64 (.f64 (fma.f64 y (sqrt.f64 x) 1) (fma.f64 y (sqrt.f64 x) 1)) (*.f64 x x))) (cbrt.f64 (+.f64 (fma.f64 y (sqrt.f64 x) 1) x))))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
✓	25.0b	(*.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2)) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)))

Compiler

Compiled 8398 to 5371 computations (36% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 x) 1)
	0.4b	(cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x))
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) 3)

series7.1s (73.2%)

Counts

1 → 15

Calls

1 calls:

7.1s	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) 3)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`cbrt-prod_binary64`
8×	`cube-prod_binary64`
8×	`unpow-prod-down_binary64`

Counts

1 → 38

Calls

1 calls:

3.0ms

(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) 3)

simplify82.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-l_binary64`
510×	`associate-r_binary64`
342×	`log-prod_binary64`
293×	`fma-neg_binary64`
255×	`exp-prod_binary64`

Counts

53 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	1376
1	286	1108
2	766	1071
3	3614	893
4	4750	893
5	5045	893

prune108.0ms (1.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	118	8	126

Error

0.0b

Counts

126 → 8

Alt Table

Status	Error	Program
	1.3b	(.f64 (pow.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)))) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x))) 3))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	25.0b	(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2))) (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2))) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x))))
	34.8b	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
✓	0.9b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) 3)
	25.1b	(.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2)) (/.f64 (cbrt.f64 (-.f64 (.f64 (fma.f64 y (sqrt.f64 x) 1) (fma.f64 y (sqrt.f64 x) 1)) (*.f64 x x))) (cbrt.f64 (+.f64 (fma.f64 y (sqrt.f64 x) 1) x))))
	45.1b	(/.f64 (neg.f64 (sqrt.f64 x)) (/.f64 -1 y))
✓	25.0b	(*.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 2)) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)))

Compiler

Compiled 3502 to 2160 computations (38.3% saved)

regimes173.0ms (1.8%)

Accuracy

Total 0.1b remaining (67.7%)

Threshold costs 0.1b (67.7%)

Counts

53 → 1

Compiler

Compiled 3143 to 2212 computations (29.6% saved)

simplify2.0ms (0%)

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	8	12
1	14	12
2	18	12
3	20	12
4	21	12
5	20	12

end125.0ms (1.3%)

Compiler: Compiled 196 to 131 computations (33.2% saved)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Details

analyze77.0ms (0.8%)

sample952.0ms (9.8%)

simplify97.0ms (1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series7.0ms (0.1%)

rewrite1.0ms (0%)

simplify50.0ms (0.5%)

prune53.0ms (0.5%)

localize7.0ms (0.1%)

series63.0ms (0.6%)

rewrite10.0ms (0.1%)

simplify63.0ms (0.7%)

prune122.0ms (1.3%)

localize10.0ms (0.1%)

series199.0ms (2%)

rewrite24.0ms (0.2%)

simplify133.0ms (1.4%)

prune229.0ms (2.4%)

localize7.0ms (0.1%)

series7.1s (73.2%)

rewrite5.0ms (0.1%)

simplify82.0ms (0.8%)

prune108.0ms (1.1%)

regimes173.0ms (1.8%)

simplify2.0ms (0%)

end125.0ms (1.3%)

Profiling

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10