Details

analyze1.3s (25.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample2.3s (45.6%)

Results

980.0ms	6241×	body	128	valid
596.0ms	857×	body	2048	valid
292.0ms	510×	body	1024	valid
201.0ms	263×	body	4096	valid
109.0ms	255×	body	512	valid
43.0ms	130×	body	256	valid

Compiler

Compiled 75 to 54 computations (28% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	31	24
2	39	22
3	45	22
4	47	22
5	49	22
6	50	22
7	47	22

prune3.0ms (0.1%)

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

12.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.4b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 68 to 48 computations (29.4% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	0.7b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	11.7b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series90.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

43.0ms

(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 4 p))))) 1/2))

32.0ms

(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 4 p))))) 1/2)

14.0ms

(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 4 p))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`sqrt-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`

Counts

3 → 40

Calls

3 calls:

1.0ms

(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 4 p))))

1.0ms

(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 4 p))))) 1/2))

0.0ms

(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 4 p))))) 1/2)

simplify98.0ms (2%)

Algorithm

1×	egg-herbie

Rules

586×	`associate-/l*_binary64`
524×	`associate-/r*_binary64`
449×	`fma-def_binary64`
357×	`fma-neg_binary64`
304×	`cancel-sign-sub-inv_binary64`

Counts

112 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	2620
1	544	2498
2	1742	2405
3	4865	2405
4	4961	2405

prune127.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	144	5	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	5	150

Error

2.0b

Counts

150 → 5

Alt Table

Status	Error	Program
▶	12.4b	(sqrt.f64 (log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	56.5b	(sqrt.f64 (fma.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 (/.f64 p x) (/.f64 p x) (fma.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35 (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3)))))
	51.8b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	53.1b	(sqrt.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
	53.7b	(neg.f64 (/.f64 p x))

Compiler

Compiled 3417 to 2360 computations (30.9% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	0.7b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	0.7b	(log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))
	11.7b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series68.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

34.0ms	(sqrt.f64 (log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
34.0ms	(log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`log-pow_binary64`
7×	`sqrt-prod_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`exp-prod_binary64`

Counts

2 → 37

Calls

2 calls:

3.0ms	(log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))
2.0ms	(sqrt.f64 (log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

972×	`times-frac_binary64`
475×	`associate-/l*_binary64`
434×	`associate-/r*_binary64`
332×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`

Counts

85 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	177	2261
1	433	2132
2	1371	2055
3	5152	2055

prune178.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	214	5	219

Error

2.0b

Counts

219 → 5

Alt Table

Status	Error	Program
✓	12.4b	(sqrt.f64 (log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	56.5b	(sqrt.f64 (fma.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 (/.f64 p x) (/.f64 p x) (fma.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35 (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3)))))
▶	51.8b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	53.1b	(sqrt.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
	53.7b	(neg.f64 (/.f64 p x))

Compiler

Compiled 5184 to 3687 computations (28.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 p (/.f64 (*.f64 x x) p))
✓	0.1b	(/.f64 (*.f64 x x) p)
✓	21.9b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

series59.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

37.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
12.0ms	(/.f64 (*.f64 x x) p)
10.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`times-frac_binary64`
40×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
26×	`sqrt-prod_binary64`

Counts

3 → 114

Calls

3 calls:

7.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
5.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
4.0ms	(/.f64 (*.f64 x x) p)

simplify151.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

676×	`times-frac_binary64`
393×	`associate-/l*_binary64`
381×	`associate-/l/_binary64`
365×	`unswap-sqr_binary64`
334×	`fma-neg_binary64`

Counts

186 → 192

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	170	2504
1	300	2325
2	853	2121
3	3029	2022
4	4200	1918
5	4963	1918
6	4993	1918

prune57.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	194	3	197

Error

Counts

197 → 3

Alt Table

Status	Error	Program
▶	53.2b	(/.f64 p x)
✓	12.4b	(sqrt.f64 (log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	53.7b	(neg.f64 (/.f64 p x))

Compiler

Compiled 2757 to 771 computations (72% saved)

localize2.0ms (0%)

prune2.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	53.2b	(/.f64 p x)
✓	12.4b	(sqrt.f64 (log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	53.7b	(neg.f64 (/.f64 p x))

Compiler

Compiled 30 to 21 computations (30% saved)

regimes381.0ms (7.7%)

Accuracy

Total 5.9b remaining (98.7%)

Threshold costs 0b (0%)

Counts

52 → 2

Compiler

Compiled 5143 to 3968 computations (22.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	61
1	28	61
2	28	61

end73.0ms (1.5%)

Compiler: Compiled 114 to 75 computations (34.2% saved)

Details

analyze1.3s (25.5%)

sample2.3s (45.6%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize12.0ms (0.2%)

series90.0ms (1.8%)

rewrite4.0ms (0.1%)

simplify98.0ms (2%)

prune127.0ms (2.6%)

localize17.0ms (0.4%)

series68.0ms (1.4%)

rewrite8.0ms (0.2%)

simplify62.0ms (1.2%)

prune178.0ms (3.6%)

localize6.0ms (0.1%)

series59.0ms (1.2%)

rewrite23.0ms (0.5%)

simplify151.0ms (3.1%)

prune57.0ms (1.1%)

localize2.0ms (0%)

prune2.0ms (0%)

regimes381.0ms (7.7%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end73.0ms (1.5%)

Profiling