Details

analyze1.8s (21.8%)

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)

sample3.2s (38.4%)

Results

1.4s	6299×	body	128	valid
794.0ms	798×	body	2048	valid
421.0ms	477×	body	1024	valid
346.0ms	302×	body	4096	valid
154.0ms	270×	body	512	valid
43.0ms	110×	body	256	valid

Compiler

Compiled 75 to 54 computations (28% saved)

simplify20.0ms (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

prune6.0ms (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

11.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.2b	(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)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
✓	0.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	0.6b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	12.6b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series213.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

75.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
59.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
55.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
24.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
18×	`sqrt-prod_binary64`

Counts

4 → 81

Calls

4 calls:

6.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
2.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))
2.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
1.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)

simplify209.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

716×	`associate-/l*_binary64`
593×	`fma-def_binary64`
419×	`cancel-sign-sub-inv_binary64`
284×	`fma-neg_binary64`
229×	`sub-neg_binary64`

Counts

177 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	4370
1	734	4162
2	2294	4048
3	5226	4048

prune367.0ms (4.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	236	5	241
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	236	6	242

Error

2.4b

Counts

242 → 6

Alt Table

Status	Error	Program
▶	11.7b	(sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3)))
	52.3b	(/.f64 p (neg.f64 x))
	52.1b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	57.5b	(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 4) (pow.f64 x 4)) -3 (*.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35)))))
✓	11.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	56.8b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))

Compiler

Compiled 5838 to 3938 computations (32.5% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3)
✓	0.5b	(cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3))
✓	0.6b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2)
✓	12.6b	(sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))

series183.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

63.0ms	(pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3)
46.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2)
44.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3))
30.0ms	(sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

4 → 73

Calls

4 calls:

3.0ms	(pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3)
3.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3))
2.0ms	(sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))
1.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2)

simplify229.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

760×	`times-frac_binary64`
633×	`fma-neg_binary64`
388×	`fma-def_binary64`
259×	`cancel-sign-sub-inv_binary64`
203×	`unswap-sqr_binary64`

Counts

169 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	4114
1	539	3786
2	1593	3641
3	4500	3641
4	5010	3641

prune283.0ms (3.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	159	6	165

Error

2.4b

Counts

165 → 6

Alt Table

Status	Error	Program
✓	11.7b	(sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3)))
	52.3b	(/.f64 p (neg.f64 x))
▶	52.1b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	57.5b	(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 4) (pow.f64 x 4)) -3 (*.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35)))))
✓	11.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	56.8b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))

Compiler

Compiled 4266 to 2980 computations (30.1% saved)

localize22.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 p (/.f64 (*.f64 x x) p))
✓	0.2b	(/.f64 (*.f64 x x) p)
✓	21.0b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

series77.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

42.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
22.0ms	(/.f64 (*.f64 x x) p)
13.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

rewrite39.0ms (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:

10.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
10.0ms	(/.f64 (*.f64 x x) p)
6.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

simplify237.0ms (2.8%)

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

prune91.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	193	5	198

Error

0.0b

Counts

198 → 5

Alt Table

Status	Error	Program
✓	11.7b	(sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3)))
▶	52.3b	(/.f64 p (neg.f64 x))
✓	11.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	54.0b	(/.f64 p x)
	56.8b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))

Compiler

Compiled 2835 to 832 computations (70.7% saved)

localize10.0ms (0.1%)

prune8.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Error

0.0b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	11.7b	(sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3)))
✓	52.3b	(/.f64 p (neg.f64 x))
✓	11.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	54.0b	(/.f64 p x)
	56.8b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))

Compiler

Compiled 78 to 58 computations (25.6% saved)

regimes1.1s (12.7%)

Accuracy

Total 6.8b remaining (99.4%)

Threshold costs 0b (0%)

Counts

67 → 2

Compiler

Compiled 7157 to 5488 computations (23.3% saved)

bsearch4.0ms (0%)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
1×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	55
1	30	55
2	33	55
3	36	55
4	39	55
5	40	55
6	39	55

end199.0ms (2.4%)

Compiler: Compiled 154 to 108 computations (29.9% saved)

Details

analyze1.8s (21.8%)

sample3.2s (38.4%)

simplify20.0ms (0.2%)

prune6.0ms (0.1%)

localize23.0ms (0.3%)

series213.0ms (2.5%)

rewrite20.0ms (0.2%)

simplify209.0ms (2.5%)

prune367.0ms (4.3%)

localize26.0ms (0.3%)

series183.0ms (2.2%)

rewrite18.0ms (0.2%)

simplify229.0ms (2.7%)

prune283.0ms (3.4%)

localize22.0ms (0.3%)

series77.0ms (0.9%)

rewrite39.0ms (0.5%)

simplify237.0ms (2.8%)

prune91.0ms (1.1%)

localize10.0ms (0.1%)

prune8.0ms (0.1%)

regimes1.1s (12.7%)

bsearch4.0ms (0%)

simplify8.0ms (0.1%)

end199.0ms (2.4%)

Profiling