Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.5s (36.2%)

Results

676.0ms	2067×	body	1024	valid
393.0ms	4358×	body	128	valid
241.0ms	1070×	body	512	valid
86.0ms	535×	body	256	valid
80.0ms	226×	body	2048	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

31.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	4.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series23.0ms (0.6%)

Counts

2 → 5

Calls

2 calls:

15.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
8.0ms	(sqrt.f64 (+.f64 x 1))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`sqrt-prod_binary64`
57×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
42×	`prod-diff_binary64`
33×	`add-cube-cbrt_binary64`

Counts

2 → 95

Calls

2 calls:

7.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
2.0ms	(sqrt.f64 (+.f64 x 1))

simplify151.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1110×	`fma-neg_binary64`
566×	`unswap-sqr_binary64`
455×	`cancel-sign-sub-inv_binary64`
444×	`fma-def_binary64`
429×	`associate-l_binary64`

Counts

100 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	2533
1	224	1344
2	592	1128
3	2527	1125
4	4099	1093
5	4381	1093
6	4663	1093
7	4949	1093
8	4730	1093

prune102.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	4	99

Error

0.1b

Counts

99 → 4

Alt Table

Status	Error	Program
	31.7b	(-.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3)) (sqrt.f64 x))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	31.5b	(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
	31.5b	(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))

Compiler

Compiled 1938 to 1044 computations (46.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series30.0ms (0.7%)

Counts

3 → 6

Calls

3 calls:

14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 1 x))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64`
28×	`sqrt-prod_binary64`
22×	`distribute-lft-out_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`

Counts

3 → 91

Calls

3 calls:

8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
2.0ms	(sqrt.f64 (+.f64 1 x))

simplify128.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-neg_binary64`
558×	`cancel-sign-sub-inv_binary64`
538×	`times-frac_binary64`
389×	`associate-l_binary64`
311×	`associate-r_binary64`

Counts

97 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	1310
1	203	1217
2	444	1211
3	1133	1207
4	2556	1207
5	4229	1207
6	4956	1207
7	4998	1207
8	4837	1207

prune125.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	87	8	95
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	90	9	99

Error

0.0b

Counts

99 → 9

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	0.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	31.7b	(-.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3)) (sqrt.f64 x))
	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	10.1b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	10.0b	(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3)) (sqrt.f64 x)))
	10.0b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	10.0b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 x) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

Compiler

Compiled 1964 to 1416 computations (27.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

series23.0ms (0.5%)

Counts

2 → 2

Calls

2 calls:

14.0ms	(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
23×	`sqrt-prod_binary64`
20×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

2 → 69

Calls

2 calls:

7.0ms	(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
7.0ms	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

simplify125.0ms (3%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-neg_binary64`
337×	`sub-neg_binary64`
335×	`associate-/l*_binary64`
331×	`times-frac_binary64`
317×	`distribute-rgt-in_binary64`

Counts

71 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	1097
1	123	1012
2	242	1012
3	510	1010
4	1229	1010
5	2371	1010
6	4345	1010
7	4559	1010
8	4920	1010
9	4820	1010

prune140.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	95	9	104

Error

0.0b

Counts

104 → 9

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	0.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
▶	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	10.1b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	10.0b	(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3)) (sqrt.f64 x)))
	9.2b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) 3))
	10.0b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	10.0b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 x) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

Compiler

Compiled 1948 to 1395 computations (28.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

series42.0ms (1%)

Counts

2 → 2

Calls

2 calls:

28.0ms

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

14.0ms

(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite79.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`sqrt-prod_binary64`
236×	`*-un-lft-identity_binary64`
148×	`times-frac_binary64`
144×	`add-sqr-sqrt_binary64`
84×	`distribute-lft-out_binary64`

Counts

2 → 204

Calls

2 calls:

32.0ms

(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

8.0ms

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

simplify222.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

635×	`unswap-sqr_binary64`
539×	`times-frac_binary64`
411×	`div-sub_binary64`
403×	`fma-def_binary64`
378×	`associate-/l*_binary64`

Counts

206 → 200

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	111	4253
1	186	4015
2	493	3961
3	1230	3833
4	2521	3833
5	4243	3833
6	4256	3829
7	4926	3829
8	4788	3829

prune635.0ms (15.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	381	6	387
Fresh	5	2	7
Picked	1	0	1
Done	1	0	1
Total	388	8	396

Error

Counts

396 → 8

Alt Table

Status	Error	Program
	0.9b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (*.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))
	0.6b	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
	10.0b	(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3)) (sqrt.f64 x)))
	0.2b	(*.f64 (sqrt.f64 1) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.5b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (*.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
	10.0b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.2b	(/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.3b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))))

Compiler

Compiled 11584 to 8573 computations (26% saved)

regimes579.0ms (13.9%)

Accuracy

Total 0.1b remaining (85.5%)

Threshold costs 0.1b (85.5%)

Counts

241 → 1

Compiler

Compiled 12496 to 9302 computations (25.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	19	16
2	27	16
3	33	16
4	35	16
5	34	16

end162.0ms (3.9%)

Compiler: Compiled 261 to 200 computations (23.4% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze3.0ms (0.1%)

sample1.5s (36.2%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series23.0ms (0.6%)

rewrite18.0ms (0.4%)

simplify151.0ms (3.6%)

prune102.0ms (2.4%)

localize6.0ms (0.1%)

series30.0ms (0.7%)

rewrite21.0ms (0.5%)

simplify128.0ms (3.1%)

prune125.0ms (3%)

localize6.0ms (0.1%)

series23.0ms (0.5%)

rewrite18.0ms (0.4%)

simplify125.0ms (3%)

prune140.0ms (3.4%)

localize7.0ms (0.2%)

series42.0ms (1%)

rewrite79.0ms (1.9%)

simplify222.0ms (5.3%)

prune635.0ms (15.2%)

regimes579.0ms (13.9%)

simplify3.0ms (0.1%)

end162.0ms (3.9%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11