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 (38.2%)

Results

596.0ms	2000×	body	1024	valid
420.0ms	4433×	body	128	valid
232.0ms	1044×	body	512	valid
97.0ms	584×	body	256	valid
75.0ms	195×	body	2048	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify11.0ms (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

30.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.7b	(-.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))
✓	4.3b	(-.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))

simplify162.0ms (4.3%)

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

prune126.0ms (3.3%)

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

0.2b

Counts

99 → 4

Alt Table

Status	Error	Program
	31.0b	(+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))))
	30.8b	(*.f64 (+.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (-.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (pow.f64 x 1/4)))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	31.1b	(/.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 2076 to 1112 computations (46.4% 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)))

series32.0ms (0.8%)

Counts

3 → 6

Calls

3 calls:

16.0ms	(/.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:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

simplify135.0ms (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

prune121.0ms (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	86	9	95
Fresh	3	0	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 (fabs.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
	0.5b	(/.f64 1 (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)))
	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))))
	0.7b	(/.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))))
	8.1b	(.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)))))
	13.3b	(/.f64 1 (+.f64 (/.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (-.f64 (fma.f64 x x 1) x))) (sqrt.f64 x)))
	0.8b	(.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)))))
	0.8b	(.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 (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 1984 to 1434 computations (27.7% 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 (fabs.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
✓	0.2b	(/.f64 1 (+.f64 (fabs.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))

series34.0ms (0.9%)

Counts

2 → 2

Calls

2 calls:

29.0ms	(/.f64 1 (+.f64 (fabs.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
6.0ms	(+.f64 (fabs.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`fma-def_binary64`
12×	`times-frac_binary64`

Counts

2 → 65

Calls

2 calls:

12.0ms	(+.f64 (fabs.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
9.0ms	(/.f64 1 (+.f64 (fabs.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))

simplify114.0ms (3%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-def_binary64`
635×	`div-sub_binary64`
513×	`fma-neg_binary64`
324×	`times-frac_binary64`
274×	`distribute-rgt-in_binary64`

Counts

67 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	1142
1	126	1035
2	229	911
3	479	909
4	1159	909
5	2684	909
6	4275	909
7	4960	909
8	4756	909

prune165.0ms (4.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	116	9	125

Error

0.0b

Counts

125 → 9

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 1 (+.f64 (fabs.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
	0.5b	(/.f64 1 (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)))
	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))))
	0.7b	(/.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))))
	8.1b	(.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)))))
	13.3b	(/.f64 1 (+.f64 (/.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (-.f64 (fma.f64 x x 1) x))) (sqrt.f64 x)))
	0.8b	(.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)))))
	0.8b	(.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 (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 2433 to 1788 computations (26.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series109.0ms (2.9%)

Counts

4 → 37

Calls

4 calls:

94.0ms	(/.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)))
5.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
5.0ms	(cbrt.f64 (+.f64 1 x))
5.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
33×	`cbrt-prod_binary64`
23×	`add-cube-cbrt_binary64`
16×	`cbrt-div_binary64`

Counts

4 → 127

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
3.0ms	(sqrt.f64 (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))

simplify160.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-def_binary64`
551×	`fma-neg_binary64`
318×	`associate-l_binary64`
292×	`associate-r_binary64`
213×	`unswap-sqr_binary64`

Counts

164 → 221

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	240	3489
1	533	3077
2	1298	2765
3	3736	2476
4	4812	2476
5	4977	2415
6	4874	2415

prune459.0ms (12.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	303	2	305
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	307	7	314

Error

0.0b

Counts

314 → 7

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 1 (+.f64 (fabs.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))))
	8.1b	(.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)))))
	13.3b	(/.f64 1 (+.f64 (/.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (-.f64 (fma.f64 x x 1) x))) (sqrt.f64 x)))
	0.8b	(.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 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.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)))))

Compiler

Compiled 9004 to 6891 computations (23.5% saved)

regimes415.0ms (10.9%)

Accuracy

Total 0.1b remaining (77.5%)

Threshold costs 0.1b (77.5%)

Counts

223 → 1

Compiler

Compiled 9301 to 7068 computations (24% 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	9	16
1	13	16
2	12	16

end149.0ms (3.9%)

Compiler: Compiled 205 to 155 computations (24.4% 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 (38.2%)

simplify11.0ms (0.3%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series25.0ms (0.7%)

rewrite19.0ms (0.5%)

simplify162.0ms (4.3%)

prune126.0ms (3.3%)

localize5.0ms (0.1%)

series32.0ms (0.8%)

rewrite26.0ms (0.7%)

simplify135.0ms (3.6%)

prune121.0ms (3.2%)

localize6.0ms (0.2%)

series34.0ms (0.9%)

rewrite25.0ms (0.7%)

simplify114.0ms (3%)

prune165.0ms (4.3%)

localize10.0ms (0.3%)

series109.0ms (2.9%)

rewrite28.0ms (0.7%)

simplify160.0ms (4.2%)

prune459.0ms (12.1%)

regimes415.0ms (10.9%)

simplify2.0ms (0.1%)

end149.0ms (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