Details

analyze1.2s (22%)

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)

sample2.1s (38.9%)

Results

929.0ms	6332×	body	128	valid
526.0ms	759×	body	2048	valid
259.0ms	518×	body	1024	valid
189.0ms	256×	body	4096	valid
104.0ms	273×	body	512	valid
33.0ms	118×	body	256	valid

Compiler

Compiled 75 to 54 computations (28% saved)

simplify7.0ms (0.1%)

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

14.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.3b	(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)

localize10.0ms (0.2%)

Local error

Found 4 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))
✓	0.0b	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
✓	0.7b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	15.6b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series81.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

28.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
22.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
20.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
11.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

rewrite9.0ms (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:

3.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
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 (1.8%)

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

prune186.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	237	4	241
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	237	5	242

Error

3.4b

Counts

242 → 5

Alt Table

Status	Error	Program
	57.8b	(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)))))
	51.1b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
✓	14.3b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
▶	14.7b	(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)))
	54.9b	(/.f64 p (neg.f64 x))

Compiler

Compiled 5778 to 3890 computations (32.7% saved)

localize14.0ms (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))
✓	0.7b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2)
✓	15.6b	(sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))

series80.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

26.0ms	(pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3)
21.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3))
21.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2)
11.0ms	(sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))

rewrite10.0ms (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:

1.0ms	(pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3)
1.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3))
1.0ms	(sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))
0.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2)

simplify109.0ms (2%)

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

prune117.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	159	5	164

Error

3.4b

Counts

164 → 5

Alt Table

Status	Error	Program
	57.8b	(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)))))
	51.1b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
✓	14.3b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	54.9b	(/.f64 p (neg.f64 x))
▶	31.6b	(sqrt.f64 (cbrt.f64 (fma.f64 3/32 (*.f64 (/.f64 x p) (/.f64 x p)) (fma.f64 (/.f64 x p) 3/16 1/8))))

Compiler

Compiled 4224 to 2939 computations (30.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 x p) 3/16 1/8)
✓	0.3b	(*.f64 (/.f64 x p) (/.f64 x p))
✓	0.7b	(fma.f64 3/32 (*.f64 (/.f64 x p) (/.f64 x p)) (fma.f64 (/.f64 x p) 3/16 1/8))
✓	14.2b	(cbrt.f64 (fma.f64 3/32 (*.f64 (/.f64 x p) (/.f64 x p)) (fma.f64 (/.f64 x p) 3/16 1/8)))

series78.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

30.0ms	(cbrt.f64 (fma.f64 3/32 (*.f64 (/.f64 x p) (/.f64 x p)) (fma.f64 (/.f64 x p) 3/16 1/8)))
28.0ms	(*.f64 (/.f64 x p) (/.f64 x p))
15.0ms	(fma.f64 3/32 (*.f64 (/.f64 x p) (/.f64 x p)) (fma.f64 (/.f64 x p) 3/16 1/8))
5.0ms	(fma.f64 (/.f64 x p) 3/16 1/8)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 102

Calls

4 calls:

10.0ms	(*.f64 (/.f64 x p) (/.f64 x p))
1.0ms	(cbrt.f64 (fma.f64 3/32 (*.f64 (/.f64 x p) (/.f64 x p)) (fma.f64 (/.f64 x p) 3/16 1/8)))
0.0ms	(fma.f64 (/.f64 x p) 3/16 1/8)
0.0ms	(fma.f64 3/32 (*.f64 (/.f64 x p) (/.f64 x p)) (fma.f64 (/.f64 x p) 3/16 1/8))

simplify116.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

503×	`associate-/r/_binary64`
395×	`associate-/l/_binary64`
314×	`fma-def_binary64`
197×	`fma-neg_binary64`
171×	`associate-*r/_binary64`

Counts

198 → 197

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	239	4079
1	633	3670
2	2091	3281
3	4800	3271
4	4965	3271

prune108.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	197	5	202

Error

3.4b

Counts

202 → 5

Alt Table

Status	Error	Program
	57.8b	(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)))))
▶	51.1b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
✓	14.3b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	54.9b	(/.f64 p (neg.f64 x))
✓	31.6b	(sqrt.f64 (cbrt.f64 (fma.f64 3/32 (*.f64 (/.f64 x p) (/.f64 x p)) (fma.f64 (/.f64 x p) 3/16 1/8))))

Compiler

Compiled 5419 to 2902 computations (46.4% 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))
✓	0.2b	(/.f64 (*.f64 x x) p)
✓	23.2b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

series40.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

25.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
9.0ms	(/.f64 (*.f64 x x) p)
5.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

rewrite19.0ms (0.4%)

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:

5.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
4.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
3.0ms	(/.f64 (*.f64 x x) p)

simplify132.0ms (2.5%)

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

prune58.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	192	5	197

Error

Counts

197 → 5

Alt Table

Status	Error	Program
	57.8b	(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)))))
	52.1b	(/.f64 p x)
✓	14.3b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	54.9b	(/.f64 p (neg.f64 x))
✓	31.6b	(sqrt.f64 (cbrt.f64 (fma.f64 3/32 (*.f64 (/.f64 x p) (/.f64 x p)) (fma.f64 (/.f64 x p) 3/16 1/8))))

Compiler

Compiled 2800 to 799 computations (71.5% saved)

regimes691.0ms (12.9%)

Accuracy

Total 5.3b remaining (99%)

Threshold costs 0b (0%)

Counts

82 → 2

Compiler

Compiled 9164 to 7156 computations (21.9% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	57
1	26	57
2	26	57

end89.0ms (1.7%)

Compiler: Compiled 164 to 106 computations (35.4% saved)

Details

analyze1.2s (22%)

sample2.1s (38.9%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series81.0ms (1.5%)

rewrite9.0ms (0.2%)

simplify98.0ms (1.8%)

prune186.0ms (3.5%)

localize14.0ms (0.3%)

series80.0ms (1.5%)

rewrite10.0ms (0.2%)

simplify109.0ms (2%)

prune117.0ms (2.2%)

localize9.0ms (0.2%)

series78.0ms (1.5%)

rewrite18.0ms (0.3%)

simplify116.0ms (2.2%)

prune108.0ms (2%)

localize6.0ms (0.1%)

series40.0ms (0.7%)

rewrite19.0ms (0.4%)

simplify132.0ms (2.5%)

prune58.0ms (1.1%)

regimes691.0ms (12.9%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end89.0ms (1.7%)

Profiling