Details

analyze26.0ms (0.6%)

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)

sample26.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	59×	body	1024	valid
5.0ms	139×	body	128	valid
4.0ms	36×	body	512	valid
1.0ms	17×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify17.0ms (0.4%)

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 → 0

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

28.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	28.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
1.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite121.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

27.9b

Rules

22×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64`
8×	`add-log-exp_binary64`
6×	`flip3-+_binary64`

Counts

2 → 88

Calls

2 calls:

17.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
15.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 1566 to 875 computations (44.1% saved)

series17.0ms (0.4%)

Error

27.8b

Counts

2 → 8

Calls

2 calls:

8.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 212 to 162 computations (23.6% saved)

simplify174.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

410×	`div-sub_binary64`
399×	`fma-def_binary64`
381×	`associate-l_binary64`
312×	`associate-r_binary64`
273×	`unswap-sqr_binary64`

Counts

96 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	120	1041
1	263	1012
2	802	997
3	3255	941
4	4358	939
5	4952	939
6	4766	939

prune42.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	4	57

Error

0.2b

Counts

57 → 4

Alt Table

Status	Error	Program
	28.7b	(-.f64 (exp.f64 (*.f64 1/2 (log1p.f64 x))) (sqrt.f64 x))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	28.6b	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	28.6b	(-.f64 (exp.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1)

Compiler

Compiled 770 to 528 computations (31.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite186.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`flip3-+_binary64`
12×	`pow1_binary64`

Counts

3 → 137

Calls

3 calls:

13.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
12.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 1964 to 1404 computations (28.5% saved)

series18.0ms (0.4%)

Error

0.2b

Counts

3 → 11

Calls

3 calls:

6.0ms	(sqrt.f64 (+.f64 1 x))
4.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
4.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 239 to 197 computations (17.6% saved)

simplify156.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1048×	`fma-neg_binary64`
347×	`fma-def_binary64`
280×	`cancel-sign-sub-inv_binary64`
261×	`times-frac_binary64`
184×	`unswap-sqr_binary64`

Counts

148 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1777
1	281	1610
2	889	1598
3	2835	1472
4	4208	1466
5	4864	1466
6	4997	1466
7	4874	1466

prune130.0ms (3.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	54	10	64
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	58	10	68

Error

0.0b

Counts

68 → 10

Alt Table

Status	Error	Program
	0.7b	(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.3b	(/.f64 1 (+.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (sqrt.f64 (cbrt.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)))))
	10.2b	(+.f64 (/.f64 (+.f64 1 x) (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (/.f64 (-.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))))
	0.3b	(*.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))
▶	0.2b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
	0.5b	(*.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	9.7b	(cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3))
	0.3b	(/.f64 1 (+.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	0.3b	(/.f64 1 (+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x)))

Compiler

Compiled 1143 to 818 computations (28.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
0.3b	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)

rewrite232.0ms (5.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

27×	`add-cube-cbrt_binary64`
24×	`add-sqr-sqrt_binary64`
14×	`pow1_binary64`
12×	`add-log-exp_binary64`
12×	`add-cbrt-cube_binary64`

Counts

4 → 157

Calls

4 calls:

14.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
12.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
12.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
11.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 2160 to 1588 computations (26.5% saved)

series27.0ms (0.6%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 1 x))
5.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
4.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))

Compiler

Compiled 348 to 295 computations (15.2% saved)

simplify129.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-neg_binary64`
425×	`cancel-sign-sub-inv_binary64`
380×	`fma-def_binary64`
378×	`associate-l_binary64`
302×	`associate-r_binary64`

Counts

172 → 72

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	1835
1	296	1754
2	859	1686
3	2878	1585
4	4818	1585
5	4829	1585

prune81.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	73	9	82

Error

0.0b

Counts

82 → 9

Alt Table

Status	Error	Program
	10.2b	(+.f64 (/.f64 (+.f64 1 x) (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (/.f64 (-.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))))
	0.7b	(sqrt.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2)) -2) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2)))
▶	0.3b	(/.f64 1 (+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x)))
	0.3b	(sqrt.f64 (pow.f64 (+.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)) -2))
	0.7b	(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (cbrt.f64 (+.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	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
	9.7b	(cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3))
	0.3b	(/.f64 1 (+.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))

Compiler

Compiled 1255 to 916 computations (27% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 1 x) 1/4)
0.0b	(+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x)))
0.3b	(*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4))

rewrite287.0ms (6.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

36×	`add-cube-cbrt_binary64`
18×	`add-cbrt-cube_binary64`
17×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`

Counts

4 → 173

Calls

4 calls:

18.0ms	(+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x))
18.0ms	(/.f64 1 (+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x)))
16.0ms	(pow.f64 (+.f64 1 x) 1/4)
15.0ms	(*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4))

Compiler

Compiled 3731 to 2896 computations (22.4% saved)

series41.0ms (1%)

Error

0.0b

Counts

4 → 20

Calls

4 calls:

12.0ms	(pow.f64 (+.f64 1 x) 1/4)
5.0ms	(*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4))
4.0ms	(/.f64 1 (+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x)))
4.0ms	(+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x))

Compiler

Compiled 715 to 589 computations (17.6% saved)

simplify136.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary64`
431×	`fma-def_binary64`
305×	`times-frac_binary64`
236×	`*-commutative_binary64`
194×	`associate-/l*_binary64`

Counts

193 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	192	2399
1	434	1993
2	1276	1935
3	3751	1862
4	4858	1862
5	4869	1862

prune149.0ms (3.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	106	9	115

Error

0.0b

Counts

115 → 9

Alt Table

Status	Error	Program
	0.3b	(/.f64 1 (+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 1 x) 1/4))) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x)))
	10.2b	(+.f64 (/.f64 (+.f64 1 x) (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (/.f64 (-.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))))
	0.7b	(sqrt.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2)) -2) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2)))
	0.7b	(/.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x)))))
	0.3b	(/.f64 1 (+.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	0.7b	(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2))) (cbrt.f64 (+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (sqrt.f64 x))))
	0.3b	(/.f64 1 (+.f64 (*.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4)) (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	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))

Compiler

Compiled 1515 to 1124 computations (25.8% saved)

regimes1.2s (27.5%)

Accuracy

Total 0.1b remaining (80.4%)

Threshold costs 0.1b (80.4%)

Compiler

Compiled 9759 to 7756 computations (20.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	16	16
2	15	16

end1.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

sample1.0s (24%)

Algorithm

1×

intervals

Results

288.0ms	2070×	body	1024	valid
158.0ms	4192×	body	128	valid
99.0ms	991×	body	512	valid
43.0ms	239×	body	2048	valid
37.0ms	508×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 259 to 198 computations (23.6% 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

analyze26.0ms (0.6%)

sample26.0ms (0.6%)

simplify17.0ms (0.4%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite121.0ms (2.9%)

series17.0ms (0.4%)

simplify174.0ms (4.2%)

prune42.0ms (1%)

localize7.0ms (0.2%)

rewrite186.0ms (4.4%)

series18.0ms (0.4%)

simplify156.0ms (3.7%)

prune130.0ms (3.1%)

localize7.0ms (0.2%)

rewrite232.0ms (5.5%)

series27.0ms (0.6%)

simplify129.0ms (3.1%)

prune81.0ms (1.9%)

localize10.0ms (0.2%)

rewrite287.0ms (6.9%)

series41.0ms (1%)

simplify136.0ms (3.3%)

prune149.0ms (3.6%)

regimes1.2s (27.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.0s (24%)

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