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)

sample1.4s (37.7%)

Results

577.0ms	2040×	body	1024	valid
387.0ms	4459×	body	128	valid
221.0ms	1026×	body	512	valid
75.0ms	510×	body	256	valid
74.0ms	221×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% 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 (0.1%)

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

29.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	1.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series24.0ms (0.7%)

Counts

2 → 5

Calls

2 calls:

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

rewrite17.0ms (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:

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

simplify148.0ms (4.1%)

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

prune101.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	3	99

Error

0.2b

Counts

99 → 3

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	29.7b	(+.f64 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (sqrt.f64 (cbrt.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)))))
	29.6b	(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))

Compiler

Compiled 1978 to 1052 computations (46.8% saved)

localize5.0ms (0.1%)

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)))

series29.0ms (0.8%)

Counts

3 → 6

Calls

3 calls:

13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
8.0ms	(sqrt.f64 (+.f64 1 x))

rewrite20.0ms (0.6%)

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:

7.0ms	(/.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))

simplify131.0ms (3.6%)

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

prune118.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	86	9	95
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	88	10	98

Error

0.0b

Counts

98 → 10

Alt Table

Status	Error	Program
	12.4b	(/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)))
	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)))))
	29.6b	(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
	2.5b	(exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
▶	0.2b	(/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))
	12.4b	(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)))))
	0.2b	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (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))))
	12.4b	(.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)))))
	0.4b	(/.f64 1 (+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))

Compiler

Compiled 1936 to 1404 computations (27.5% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series160.0ms (4.4%)

Counts

3 → 3

Calls

3 calls:

115.0ms	(/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))
25.0ms	(+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))
19.0ms	(hypot.f64 1 (sqrt.f64 x))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
7×	`add-exp-log_binary64`

Counts

3 → 66

Calls

3 calls:

4.0ms	(+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))
4.0ms	(/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))
0.0ms	(hypot.f64 1 (sqrt.f64 x))

simplify92.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

684×	`fma-def_binary64`
672×	`div-sub_binary64`
530×	`associate-l_binary64`
336×	`distribute-rgt-in_binary64`
309×	`associate-+l+_binary64`

Counts

69 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1114
1	129	1029
2	221	1023
3	439	1021
4	963	1021
5	2310	1021
6	4448	1021
7	5094	1021

prune131.0ms (3.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	91	10	101

Error

0.0b

Counts

101 → 10

Alt Table

Status	Error	Program
	12.4b	(/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)))
	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)))))
	29.6b	(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
	2.5b	(exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.4b	(/.f64 1 (fma.f64 (*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x)))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (sqrt.f64 x)))
	12.4b	(.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 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))
	12.4b	(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)))))
▶	0.2b	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (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))))

Compiler

Compiled 1917 to 1224 computations (36.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series96.0ms (2.7%)

Counts

4 → 37

Calls

4 calls:

81.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
6.0ms	(sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
5.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
4.0ms	(cbrt.f64 (+.f64 1 x))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
28×	`cbrt-prod_binary64`
26×	`cbrt-div_binary64`
21×	`add-cube-cbrt_binary64`

Counts

4 → 133

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
7.0ms	(sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
2.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
2.0ms	(cbrt.f64 (+.f64 1 x))

simplify164.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

652×	`times-frac_binary64`
561×	`fma-neg_binary64`
391×	`fma-def_binary64`
269×	`cancel-sign-sub-inv_binary64`
264×	`associate-l_binary64`

Counts

170 → 204

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	209	3488
1	420	3111
2	959	2778
3	2634	2494
4	4404	2333
5	4797	2333
6	4986	2333
7	4904	2333

prune408.0ms (11.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	282	4	286
Fresh	4	4	8
Picked	1	0	1
Done	1	0	1
Total	288	8	296

Error

0.0b

Counts

296 → 8

Alt Table

Status	Error	Program
	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))))) (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
	0.2b	(log1p.f64 (expm1.f64 (/.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)))))
	12.4b	(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)))))
	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))))
	12.4b	(.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)))))
	0.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x))))
	0.7b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x))) (cbrt.f64 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x))))) (cbrt.f64 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x))))

Compiler

Compiled 8477 to 6459 computations (23.8% saved)

regimes370.0ms (10.2%)

Accuracy

Total 0.1b remaining (82.3%)

Threshold costs 0.1b (82.3%)

Counts

190 → 1

Compiler

Compiled 9175 to 6944 computations (24.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	10	14
2	9	14

end168.0ms (4.6%)

Compiler: Compiled 279 to 212 computations (24% 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%)

sample1.4s (37.7%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series24.0ms (0.7%)

rewrite17.0ms (0.5%)

simplify148.0ms (4.1%)

prune101.0ms (2.8%)

localize5.0ms (0.1%)

series29.0ms (0.8%)

rewrite20.0ms (0.6%)

simplify131.0ms (3.6%)

prune118.0ms (3.2%)

localize5.0ms (0.1%)

series160.0ms (4.4%)

rewrite11.0ms (0.3%)

simplify92.0ms (2.5%)

prune131.0ms (3.6%)

localize10.0ms (0.3%)

series96.0ms (2.7%)

rewrite26.0ms (0.7%)

simplify164.0ms (4.5%)

prune408.0ms (11.3%)

regimes370.0ms (10.2%)

simplify2.0ms (0.1%)

end168.0ms (4.6%)

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