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)

sample52.0ms (1.4%)

Algorithm

1×

intervals

Results

8.0ms	10×	body	2048	valid
8.0ms	55×	body	1024	valid
5.0ms	135×	body	128	valid
4.0ms	38×	body	512	valid
1.0ms	18×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify10.0ms (0.3%)

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

31.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	3.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series25.0ms (0.7%)

Counts

2 → 5

Calls

2 calls:

18.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 x 1))

rewrite19.0ms (0.5%)

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:

8.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

simplify155.0ms (4.2%)

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

prune114.0ms (3.1%)

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
	31.2b	(+.f64 (fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
	30.9b	(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
	31.5b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3) (pow.f64 (sqrt.f64 x) 3)) (+.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (+.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 2038 to 1092 computations (46.4% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)))

series31.0ms (0.8%)

Counts

3 → 6

Calls

3 calls:

15.0ms	(/.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))

rewrite26.0ms (0.7%)

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:

11.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
3.0ms	(sqrt.f64 (+.f64 1 x))

simplify135.0ms (3.7%)

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 (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	92	7	99

Error

0.0b

Counts

99 → 7

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	31.5b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3) (pow.f64 (sqrt.f64 x) 3)) (+.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (+.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 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))))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	0.4b	(*.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)))))
	0.7b	(/.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))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	12.2b	(.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)))))

Compiler

Compiled 1870 to 1342 computations (28.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series169.0ms (4.6%)

Counts

4 → 37

Calls

4 calls:

148.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
11.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
5.0ms	(cbrt.f64 (+.f64 1 x))
5.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))

rewrite41.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64`
30×	`cbrt-prod_binary64`
29×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`add-cube-cbrt_binary64`

Counts

4 → 135

Calls

4 calls:

13.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
12.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
3.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))
2.0ms	(cbrt.f64 (+.f64 1 x))

simplify148.0ms (4%)

Algorithm

1×	egg-herbie

Rules

771×	`times-frac_binary64`
753×	`fma-neg_binary64`
281×	`associate-/r*_binary64`
273×	`associate-/l*_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

172 → 260

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	280	4455
1	675	3809
2	1794	3051
3	4087	2701
4	4930	2701
5	4872	2701

prune458.0ms (12.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	300	3	303
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	302	8	310

Error

0.0b

Counts

310 → 8

Alt Table

Status	Error	Program
	0.4b	(/.f64 1 (+.f64 (.f64 (fabs.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	31.5b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3) (pow.f64 (sqrt.f64 x) 3)) (+.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (+.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))))
▶	0.3b	(/.f64 1 (+.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x))) (sqrt.f64 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))))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	0.7b	(/.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))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	12.2b	(.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)))))

Compiler

Compiled 8235 to 6357 computations (22.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series28.0ms (0.8%)

Counts

3 → 17

Calls

3 calls:

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

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
27×	`cbrt-prod_binary64`
24×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
14×	`cbrt-div_binary64`

Counts

3 → 101

Calls

3 calls:

10.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x)))
10.0ms	(/.f64 1 (+.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
3.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 x)))

simplify142.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-neg_binary64`
463×	`fma-def_binary64`
333×	`cancel-sign-sub-inv_binary64`
305×	`associate-l_binary64`
275×	`distribute-rgt-in_binary64`

Counts

118 → 157

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	188	2778
1	422	2651
2	1034	2541
3	2826	2502
4	4552	2492
5	4960	2492
6	4951	2492

prune357.0ms (9.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	200	8	208

Error

0.0b

Counts

208 → 8

Alt Table

Status	Error	Program
	0.4b	(/.f64 1 (+.f64 (.f64 (fabs.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	31.5b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3) (pow.f64 (sqrt.f64 x) 3)) (+.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (+.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))
✓	0.3b	(/.f64 1 (+.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x))) (sqrt.f64 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))))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	0.7b	(/.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))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	12.2b	(.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)))))

Compiler

Compiled 5279 to 4009 computations (24.1% saved)

regimes489.0ms (13.3%)

Accuracy

Total 0.1b remaining (78.8%)

Threshold costs 0.1b (78.8%)

Counts

228 → 1

Compiler

Compiled 9988 to 7578 computations (24.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	12	14
2	11	14

end0.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample1.1s (29.5%)

Algorithm

1×

intervals

Results

384.0ms	1997×	body	1024	valid
179.0ms	4315×	body	128	valid
114.0ms	1013×	body	512	valid
38.0ms	216×	body	2048	valid
36.0ms	459×	body	256	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 231 to 174 computations (24.7% 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%)

sample52.0ms (1.4%)

simplify10.0ms (0.3%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series25.0ms (0.7%)

rewrite19.0ms (0.5%)

simplify155.0ms (4.2%)

prune114.0ms (3.1%)

localize6.0ms (0.2%)

series31.0ms (0.8%)

rewrite26.0ms (0.7%)

simplify135.0ms (3.7%)

prune125.0ms (3.4%)

localize9.0ms (0.2%)

series169.0ms (4.6%)

rewrite41.0ms (1.1%)

simplify148.0ms (4%)

prune458.0ms (12.5%)

localize9.0ms (0.2%)

series28.0ms (0.8%)

rewrite30.0ms (0.8%)

simplify142.0ms (3.9%)

prune357.0ms (9.7%)

regimes489.0ms (13.3%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (29.5%)

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