Details

analyze1.2s (20.1%)

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 (36.2%)

Results

935.0ms	6232×	body	128	valid
494.0ms	829×	body	2048	valid
265.0ms	532×	body	1024	valid
216.0ms	281×	body	4096	valid
102.0ms	263×	body	512	valid
44.0ms	119×	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

16.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.0b	(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)

localize9.0ms (0.2%)

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	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	0.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	10.7b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series102.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

30.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
29.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
28.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
15.0ms	(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)

simplify93.0ms (1.6%)

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

prune199.0ms (3.4%)

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

3.6b

Counts

242 → 6

Alt Table

Status	Error	Program
	35.8b	(fma.f64 (/.f64 x (*.f64 p (sqrt.f64 1/2))) -1/8 (sqrt.f64 1/2))
▶	16.0b	(cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)) (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))) (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	51.3b	(/.f64 p (neg.f64 x))
✓	16.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	56.1b	(sqrt.f64 (fma.f64 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) 10 (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)))))
	50.6b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

Compiler

Compiled 5861 to 3949 computations (32.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)) (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))) (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	0.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	0.4b	(.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)) (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 4 p))))) 1/2)))
	10.7b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series58.0ms (1%)

Counts

2 → 48

Calls

2 calls:

32.0ms

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

26.0ms

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

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
17×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 65

Calls

2 calls:

7.0ms

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

5.0ms

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

simplify102.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

972×	`times-frac_binary64`
731×	`fma-neg_binary64`
478×	`associate-/l*_binary64`
334×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`

Counts

113 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	3400
1	453	2907
2	1496	2680
3	4890	2678
4	5449	2678

prune543.0ms (9.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	449	1	450
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	451	5	456

Error

3.6b

Counts

456 → 5

Alt Table

Status	Error	Program
	51.3b	(/.f64 p (neg.f64 x))
✓	16.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
▶	16.0b	(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p 4))))) 1/2)) 4) 1/2) (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 4 p))))) 1/2))))
	56.1b	(sqrt.f64 (fma.f64 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) 10 (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)))))
	50.6b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

Compiler

Compiled 23520 to 16407 computations (30.2% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p 4))))) 1/2)) 4) 1/2) (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 4 p))))) 1/2))))
✓	0.4b	(pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p 4))))) 1/2)) 4)
	10.7b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))
✓	10.7b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 p 4))))

series81.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

39.0ms

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

29.0ms

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

12.0ms

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

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
6×	`unpow-prod-down_binary64`
6×	`sqrt-prod_binary64`

Counts

3 → 51

Calls

3 calls:

4.0ms

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

2.0ms

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

1.0ms

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

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

669×	`associate-/l*_binary64`
609×	`associate-/r*_binary64`
486×	`fma-def_binary64`
296×	`cancel-sign-sub-inv_binary64`
216×	`fma-neg_binary64`

Counts

123 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	3509
1	628	3141
2	1926	2828
3	5369	2828

prune233.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	218	5	223

Error

3.6b

Counts

223 → 5

Alt Table

Status	Error	Program
	51.3b	(/.f64 p (neg.f64 x))
✓	16.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	16.0b	(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p 4))))) 1/2)) 4) 1/2) (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 4 p))))) 1/2))))
	56.1b	(sqrt.f64 (fma.f64 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) 10 (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)))))
▶	50.6b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

Compiler

Compiled 8939 to 6473 computations (27.6% 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)
✓	23.7b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

series43.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

28.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
10.0ms	(/.f64 (*.f64 x x) p)
5.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

rewrite19.0ms (0.3%)

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	(/.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)

simplify133.0ms (2.3%)

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

prune55.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	193	4	197

Error

Counts

197 → 4

Alt Table

Status	Error	Program
	51.3b	(/.f64 p (neg.f64 x))
✓	16.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	16.0b	(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p 4))))) 1/2)) 4) 1/2) (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 4 p))))) 1/2))))
	50.9b	(/.f64 p x)

Compiler

Compiled 2782 to 790 computations (71.6% saved)

regimes605.0ms (10.5%)

Accuracy

Total 6.8b remaining (98.3%)

Threshold costs 0b (0%)

Counts

68 → 2

Compiler

Compiled 10954 to 8185 computations (25.3% saved)

bsearch2.0ms (0%)

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

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	49
1	24	49
2	24	49

end77.0ms (1.3%)

Compiler: Compiled 136 to 93 computations (31.6% saved)

Details

analyze1.2s (20.1%)

sample2.1s (36.2%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series102.0ms (1.8%)

rewrite9.0ms (0.2%)

simplify93.0ms (1.6%)

prune199.0ms (3.4%)

localize14.0ms (0.2%)

series58.0ms (1%)

rewrite18.0ms (0.3%)

simplify102.0ms (1.8%)

prune543.0ms (9.4%)

localize26.0ms (0.5%)

series81.0ms (1.4%)

rewrite9.0ms (0.2%)

simplify79.0ms (1.4%)

prune233.0ms (4%)

localize5.0ms (0.1%)

series43.0ms (0.7%)

rewrite19.0ms (0.3%)

simplify133.0ms (2.3%)

prune55.0ms (1%)

regimes605.0ms (10.5%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

end77.0ms (1.3%)

Profiling