Details

analyze1.2s (25.4%)

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 (44.8%)

Results

896.0ms	6239×	body	128	valid
544.0ms	870×	body	2048	valid
268.0ms	468×	body	1024	valid
211.0ms	288×	body	4096	valid
95.0ms	244×	body	512	valid
38.0ms	147×	body	256	valid

Compiler

Compiled 75 to 54 computations (28% saved)

simplify13.0ms (0.3%)

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

11.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.6b	(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	(fma.f64 x x (.f64 p (.f64 4 p)))
✓	1.0b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	16.1b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series80.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

29.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
26.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
16.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))
8.0ms	(fma.f64 x x (.f64 p (.f64 4 p)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 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 x x (.f64 p (.f64 4 p)))
0.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

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

Counts

146 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	3011
1	556	2866
2	1776	2773
3	4964	2773

prune126.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	168	4	172
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	168	5	173

Error

2.9b

Counts

173 → 5

Alt Table

Status	Error	Program
▶	11.6b	(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	54.3b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	58.1b	(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)))))
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	52.9b	(neg.f64 (/.f64 p x))

Compiler

Compiled 3851 to 2644 computations (31.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x x (.f64 p (.f64 4 p)))
✓	0.8b	(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	1.0b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
	16.1b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series28.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

27.0ms

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`log-pow_binary64`
6×	`exp-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

2.0ms

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

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

816×	`times-frac_binary64`
697×	`fma-neg_binary64`
385×	`associate-/l*_binary64`
330×	`associate-/r*_binary64`
233×	`associate-r_binary64`

Counts

44 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1298
1	297	1206
2	938	1153
3	4720	1151
4	5303	1151

prune152.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	183	5	188

Error

2.9b

Counts

188 → 5

Alt Table

Status	Error	Program
✓	11.6b	(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	54.3b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	58.1b	(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)))))
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
▶	52.9b	(neg.f64 (/.f64 p x))

Compiler

Compiled 4484 to 3194 computations (28.8% saved)

localize3.0ms (0.1%)

prune4.0ms (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

2.9b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	11.6b	(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
▶	54.3b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	58.1b	(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)))))
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	52.9b	(neg.f64 (/.f64 p x))

Compiler

Compiled 136 to 94 computations (30.9% saved)

localize5.0ms (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)
✓	23.6b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

series48.0ms (1%)

Counts

3 → 72

Calls

3 calls:

30.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
10.0ms	(/.f64 (*.f64 x x) p)
7.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

rewrite18.0ms (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:

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

simplify134.0ms (2.9%)

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 (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	0	1
Picked	1	0	1
Done	0	3	3
Total	193	4	197

Error

Counts

197 → 4

Alt Table

Status	Error	Program
✓	11.6b	(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	52.9b	(neg.f64 (/.f64 p x))
	54.8b	(/.f64 p x)

Compiler

Compiled 2763 to 776 computations (71.9% saved)

regimes474.0ms (10.2%)

Accuracy

Total 6.9b remaining (98.9%)

Threshold costs 0b (0%)

Counts

58 → 2

Compiler

Compiled 5623 to 4431 computations (21.2% saved)

bsearch1.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	51
1	30	51
2	34	51
3	37	51
4	38	51
5	38	51

end68.0ms (1.5%)

Compiler: Compiled 119 to 81 computations (31.9% saved)

Details

analyze1.2s (25.4%)

sample2.1s (44.8%)

simplify13.0ms (0.3%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series80.0ms (1.7%)

rewrite4.0ms (0.1%)

simplify76.0ms (1.6%)

prune126.0ms (2.7%)

localize13.0ms (0.3%)

series28.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify63.0ms (1.4%)

prune152.0ms (3.3%)

localize3.0ms (0.1%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series48.0ms (1%)

rewrite18.0ms (0.4%)

simplify134.0ms (2.9%)

prune57.0ms (1.2%)

regimes474.0ms (10.2%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end68.0ms (1.5%)

Profiling