Details

analyze1.1s (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)

sample1.9s (38.1%)

Results

872.0ms	6274×	body	128	valid
468.0ms	798×	body	2048	valid
252.0ms	514×	body	1024	valid
187.0ms	273×	body	4096	valid
101.0ms	261×	body	512	valid
35.0ms	136×	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

11.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.7b	(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	(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)))))
✓	0.4b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	12.1b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series93.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

27.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
26.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
24.0ms	(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)

simplify97.0ms (1.9%)

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

prune193.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	235	6	241
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	235	7	242

Error

2.5b

Counts

242 → 7

Alt Table

Status	Error	Program
▶	11.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	58.3b	(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)))))
	55.3b	(/.f64 p (neg.f64 x))
	53.7b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	12.2b	(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)))
	55.9b	(sqrt.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
✓	11.7b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 5836 to 3934 computations (32.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	0.0b	(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))
	0.4b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
	12.1b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series56.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
26.0ms	(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
0.0ms	(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))

simplify101.0ms (2%)

Algorithm

1×	egg-herbie

Rules

510×	`times-frac_binary64`
288×	`sub-neg_binary64`
266×	`fma-def_binary64`
245×	`associate-r_binary64`
229×	`unswap-sqr_binary64`

Counts

70 → 92

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	126	1675
1	345	1542
2	977	1475
3	4278	1433
4	4949	1413
5	4952	1413
6	4953	1413

prune145.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	193	5	198

Error

2.5b

Counts

198 → 5

Alt Table

Status	Error	Program
▶	12.2b	(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)))
✓	11.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	55.3b	(/.f64 p (neg.f64 x))
✓	11.7b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	54.5b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6)))))

Compiler

Compiled 4388 to 3069 computations (30.1% saved)

localize12.0ms (0.2%)

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)
✓	0.4b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2)
✓	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))
✓	12.1b	(sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))

series91.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

29.0ms	(pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3)
26.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2)
24.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2) 3))
11.0ms	(sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))

rewrite15.0ms (0.3%)

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)

simplify108.0ms (2.1%)

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	541	3786
2	1595	3641
3	4502	3641
4	5010	3641

prune117.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	159	5	164

Error

2.5b

Counts

164 → 5

Alt Table

Status	Error	Program
✓	12.2b	(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)))
✓	11.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	55.3b	(/.f64 p (neg.f64 x))
✓	11.7b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
▶	54.5b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6)))))

Compiler

Compiled 4071 to 2802 computations (31.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 p x) 4)
✓	0.2b	(pow.f64 (/.f64 x p) 6)
✓	17.9b	(fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6))))
✓	20.1b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6)))))

series118.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

41.0ms	(fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6))))
33.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6)))))
26.0ms	(pow.f64 (/.f64 x p) 6)
18.0ms	(pow.f64 (/.f64 p x) 4)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`unpow-prod-down_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`

Counts

4 → 85

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 p x) 4)
3.0ms	(pow.f64 (/.f64 x p) 6)
1.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6)))))
0.0ms	(fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6))))

simplify102.0ms (2%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/l*_binary64`
354×	`fma-neg_binary64`
337×	`fma-def_binary64`
237×	`cancel-sign-sub-inv_binary64`
200×	`sqr-pow_binary64`

Counts

181 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	3813
1	567	3294
2	1768	3221
3	4767	3217
4	4992	3217

prune94.0ms (1.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	160	6	166

Error

Counts

166 → 6

Alt Table

Status	Error	Program
✓	12.2b	(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)))
✓	11.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	52.9b	(/.f64 p x)
	55.3b	(/.f64 p (neg.f64 x))
✓	11.7b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	54.5b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6)))))

Compiler

Compiled 4657 to 2591 computations (44.4% saved)

regimes532.0ms (10.4%)

Accuracy

Total 7.0b remaining (99.7%)

Threshold costs 0b (0%)

Counts

96 → 2

Compiler

Compiled 9870 to 7648 computations (22.5% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	53
1	27	53
2	26	53

end95.0ms (1.9%)

Compiler: Compiled 165 to 110 computations (33.3% saved)

Details

analyze1.1s (22%)

sample1.9s (38.1%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series93.0ms (1.8%)

rewrite9.0ms (0.2%)

simplify97.0ms (1.9%)

prune193.0ms (3.8%)

localize11.0ms (0.2%)

series56.0ms (1.1%)

rewrite1.0ms (0%)

simplify101.0ms (2%)

prune145.0ms (2.8%)

localize12.0ms (0.2%)

series91.0ms (1.8%)

rewrite15.0ms (0.3%)

simplify108.0ms (2.1%)

prune117.0ms (2.3%)

localize10.0ms (0.2%)

series118.0ms (2.3%)

rewrite12.0ms (0.2%)

simplify102.0ms (2%)

prune94.0ms (1.8%)

regimes532.0ms (10.4%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end95.0ms (1.9%)

Profiling