Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample2.2s (32.8%)

Results

1.1s	2184×	body	2048	valid
491.0ms	4289×	body	128	valid
397.0ms	1020×	body	1024	valid
150.0ms	504×	body	512	valid
49.0ms	259×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	35	15
4	42	15
5	52	15
6	60	15
7	69	15
8	72	15
9	53	15

prune3.0ms (0%)

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

14.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	1.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series16.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
4.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
2.0ms	(hypot.f64 1 x)

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
24×	`sqrt-prod_binary64`
21×	`prod-diff_binary64`

Counts

4 → 110

Calls

4 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
2.0ms	(/.f64 1/2 (hypot.f64 1 x))
0.0ms	(hypot.f64 1 x)

simplify129.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
463×	`fma-neg_binary64`
398×	`times-frac_binary64`
372×	`associate-l_binary64`
332×	`associate-r_binary64`

Counts

158 → 196

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	3244
1	653	2896
2	1805	2575
3	4560	2539
4	4860	2539
5	5266	2539

prune190.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	193	4	197

Error

0.0b

Counts

197 → 4

Alt Table

Status	Error	Program
	15.0b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	34.0b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
	15.0b	(*.f64 (+.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (-.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
▶	14.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

Compiler

Compiled 4491 to 3990 computations (11.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	1.1b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series32.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

24.0ms

(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

5.0ms

(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

3.0ms

(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
80×	`times-frac_binary64`
60×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

3 → 157

Calls

3 calls:

14.0ms

(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

10.0ms

(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

9.0ms

(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify155.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

565×	`times-frac_binary64`
260×	`fma-def_binary64`
206×	`associate-r_binary64`
200×	`associate-/r*_binary64`
184×	`fma-neg_binary64`

Counts

193 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	8251
1	1249	5965
2	3887	5923
3	5050	5923

prune355.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	335	2	337
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	337	4	341

Error

0.0b

Counts

341 → 4

Alt Table

Status	Error	Program
	28.9b	(/.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (neg.f64 (.f64 (/.f64 (sqrt.f64 1/2) (hypot.f64 1 x)) (/.f64 (sqrt.f64 1/2) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (hypot.f64 1 x))) (/.f64 (sqrt.f64 1/2) 1) (*.f64 (/.f64 (sqrt.f64 1/2) (hypot.f64 1 x)) (/.f64 (sqrt.f64 1/2) 1)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	14.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
▶	15.0b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	34.0b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))

Compiler

Compiled 11765 to 10505 computations (10.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	1.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`sqrt-prod_binary64`
73×	`add-sqr-sqrt_binary64`
53×	`*-un-lft-identity_binary64`
24×	`difference-of-squares_binary64`
23×	`swap-sqr_binary64`

Counts

1 → 90

Calls

1 calls:

44.0ms

(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

simplify116.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-neg_binary64`
724×	`cancel-sign-sub-inv_binary64`
298×	`associate-l_binary64`
255×	`sub-neg_binary64`
254×	`associate-r_binary64`

Counts

102 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	2810
1	311	2556
2	949	2466
3	2904	2417
4	4965	2417
5	5323	2417

prune485.0ms (7.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	434	1	435
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	436	3	439

Error

0.0b

Counts

439 → 3

Alt Table

Status	Error	Program
▶	14.9b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))))))
✓	14.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	34.0b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))

Compiler

Compiled 15332 to 13880 computations (9.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))))))
✓	1.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))))
	1.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	3.8b	(log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))

series15.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

6.0ms

(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))))))

6.0ms

(-.f64 1 (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))))

3.0ms

(log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))

rewrite52.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-sqr-sqrt_binary64`
67×	`*-un-lft-identity_binary64`
59×	`sqrt-prod_binary64`
32×	`add-cube-cbrt_binary64`
24×	`prod-diff_binary64`

Counts

3 → 139

Calls

3 calls:

25.0ms

(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))))))

9.0ms

(-.f64 1 (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))))

5.0ms

(log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))

simplify137.0ms (2%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-neg_binary64`
467×	`fma-def_binary64`
416×	`associate-l_binary64`
368×	`associate-r_binary64`
185×	`associate-/r*_binary64`

Counts

175 → 210

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	294	4006
1	536	3825
2	1469	3709
3	4569	3709
4	4988	3709

prune406.0ms (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	274	2	276
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	275	4	279

Error

0.0b

Counts

279 → 4

Alt Table

Status	Error	Program
	14.9b	(/.f64 (.f64 (sqrt.f64 (-.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))) (sqrt.f64 (-.f64 (.f64 1 1) (.f64 (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))))))) (.f64 (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))))))))
✓	14.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	14.9b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	34.0b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))

Compiler

Compiled 11479 to 10487 computations (8.6% saved)

regimes2.0s (29.8%)

Accuracy

Total 0.0b remaining (16.8%)

Threshold costs 0.0b (16.8%)

Counts

200 → 3

Compiler

Compiled 36703 to 33619 computations (8.4% saved)

bsearch52.0ms (0.8%)

Steps

Iters	Range		Point
10	2.9044665788828883e-6	1499032.0924529708	0.002254868162487943
10	-0.03470345168262622	-4.4981372541030017e-17	-0.0025715001607349015

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	41	88
2	51	88
3	55	88
4	57	88
5	55	88

end187.0ms (2.8%)

Compiler: Compiled 265 to 233 computations (12.1% saved)

Details

analyze1.0ms (0%)

sample2.2s (32.8%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series16.0ms (0.2%)

rewrite23.0ms (0.3%)

simplify129.0ms (1.9%)

prune190.0ms (2.8%)

localize10.0ms (0.1%)

series32.0ms (0.5%)

rewrite48.0ms (0.7%)

simplify155.0ms (2.3%)

prune355.0ms (5.3%)

localize17.0ms (0.3%)

series6.0ms (0.1%)

rewrite56.0ms (0.8%)

simplify116.0ms (1.7%)

prune485.0ms (7.2%)

localize17.0ms (0.2%)

series15.0ms (0.2%)

rewrite52.0ms (0.8%)

simplify137.0ms (2%)

prune406.0ms (6%)

regimes2.0s (29.8%)

bsearch52.0ms (0.8%)

simplify4.0ms (0.1%)

end187.0ms (2.8%)

Profiling