Details

analyze4.0ms (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)

sample2.3s (42.8%)

Results

981.0ms	2012×	body	1024	valid
668.0ms	4470×	body	128	valid
357.0ms	1029×	body	512	valid
133.0ms	529×	body	256	valid
129.0ms	216×	body	2048	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify14.0ms (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

28.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	4.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series29.0ms (0.5%)

Counts

2 → 5

Calls

2 calls:

18.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms	(sqrt.f64 (+.f64 x 1))

rewrite18.0ms (0.3%)

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))
3.0ms	(sqrt.f64 (+.f64 x 1))

simplify184.0ms (3.4%)

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

prune119.0ms (2.2%)

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

0.1b

Counts

99 → 3

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	28.1b	(fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
	28.4b	(/.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)))))

Compiler

Compiled 1986 to 1074 computations (45.9% saved)

localize6.0ms (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)))

series35.0ms (0.6%)

Counts

3 → 6

Calls

3 calls:

16.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
8.0ms	(sqrt.f64 (+.f64 1 x))

rewrite50.0ms (0.9%)

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:

14.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
5.0ms	(sqrt.f64 (+.f64 1 x))

simplify200.0ms (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

prune124.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	88	7	95
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	90	8	98

Error

0.0b

Counts

98 → 8

Alt Table

Status	Error	Program
	0.3b	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.8b	(.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))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.3b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.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))))
	7.1b	(.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)))))
	7.1b	(/.f64 1 (+.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (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)))))

Compiler

Compiled 1906 to 1376 computations (27.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series47.0ms (0.9%)

Counts

2 → 2

Calls

2 calls:

31.0ms

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

15.0ms

(*.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)))))

rewrite89.0ms (1.7%)

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)))))

9.0ms

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

simplify249.0ms (4.6%)

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

prune697.0ms (12.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	371	4	375
Fresh	4	2	6
Picked	0	1	1
Done	1	0	1
Total	376	7	383

Error

Counts

383 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.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))))))
▶	0.2b	(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))
	0.3b	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
	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 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	7.1b	(.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 (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)))))

Compiler

Compiled 11425 to 8441 computations (26.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))
	0.0b	(sqrt.f64 (+.f64 1 x))
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.2b	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series49.0ms (0.9%)

Counts

2 → 2

Calls

2 calls:

28.0ms

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

21.0ms

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

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
24×	`distribute-lft-out_binary64`
17×	`pow1_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

2 → 83

Calls

2 calls:

18.0ms

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

17.0ms

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

simplify119.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

606×	`distribute-rgt-in_binary64`
583×	`distribute-lft-in_binary64`
315×	`fma-def_binary64`
271×	`times-frac_binary64`
267×	`exp-prod_binary64`

Counts

85 → 109

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	2287
1	290	2023
2	994	1593
3	3376	1570
4	4509	1472
5	4992	1472
6	4831	1472

prune269.0ms (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	211	5	216

Error

Counts

216 → 5

Alt Table

Status	Error	Program
	0.3b	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
	0.3b	(pow.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (fma.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))) (/.f64 -1 2))
	0.1b	(pow.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) (+.f64 1 x)) (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (/.f64 -1 2))
	7.1b	(.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 (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)))))

Compiler

Compiled 5569 to 3975 computations (28.6% saved)

regimes584.0ms (10.8%)

Accuracy

Total 0.1b remaining (90.3%)

Threshold costs 0.1b (90.3%)

Counts

297 → 1

Compiler

Compiled 12840 to 9609 computations (25.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	18	32
2	16	32

end125.0ms (2.3%)

Compiler: Compiled 174 to 127 computations (27% 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

analyze4.0ms (0.1%)

sample2.3s (42.8%)

simplify14.0ms (0.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series29.0ms (0.5%)

rewrite18.0ms (0.3%)

simplify184.0ms (3.4%)

prune119.0ms (2.2%)

localize6.0ms (0.1%)

series35.0ms (0.6%)

rewrite50.0ms (0.9%)

simplify200.0ms (3.7%)

prune124.0ms (2.3%)

localize8.0ms (0.1%)

series47.0ms (0.9%)

rewrite89.0ms (1.7%)

simplify249.0ms (4.6%)

prune697.0ms (12.9%)

localize10.0ms (0.2%)

series49.0ms (0.9%)

rewrite42.0ms (0.8%)

simplify119.0ms (2.2%)

prune269.0ms (5%)

regimes584.0ms (10.8%)

simplify2.0ms (0%)

end125.0ms (2.3%)

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