Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.3s (13.7%)

Results

588.0ms	2206×	body	1024	valid
379.0ms	4427×	body	128	valid
208.0ms	1039×	body	512	valid
86.0ms	584×	body	256	valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify12.0ms (0.1%)

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 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

22.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	22.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	4.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series48.0ms (0.5%)

Counts

4 → 8

Calls

4 calls:

15.0ms	(/.f64 1 (sqrt.f64 x))
15.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(sqrt.f64 (+.f64 x 1))

rewrite231.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

1084×	`times-frac_binary64`
922×	`*-un-lft-identity_binary64`
802×	`add-sqr-sqrt_binary64`
728×	`add-cube-cbrt_binary64`
594×	`prod-diff_binary64`

Counts

4 → 815

Calls

4 calls:

45.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

simplify834.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

814×	`fma-neg_binary64`
623×	`fma-def_binary64`
489×	`cancel-sign-sub-inv_binary64`
358×	`associate-r_binary64`
241×	`times-frac_binary64`

Counts

823 → 641

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	242	36505
1	501	25671
2	1210	18755
3	3412	17853
4	4423	17803
5	4884	17803
6	4730	17803

prune1.6s (17.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	619	22	641
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	620	22	642

Error

21.9b

Counts

642 → 22

Alt Table

Status	Error	Program
▶	22.7b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	31.2b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3))))))) (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (*.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))))))
	31.2b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))))
	31.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3))))))) (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))))))
	30.5b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))))))) (fma.f64 (neg.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 x 1))))) (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))) (.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))))))
	30.7b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))))))) (fma.f64 (neg.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 x 1))))) (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))) (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))))
	31.3b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3))))))) (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (*.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))))))
	30.5b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))))
	31.2b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))))
	31.1b	(fma.f64 (/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	30.5b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (*.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))))))
	30.7b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))))))) (fma.f64 (neg.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 x 1))))) (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))) (.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))))))
	33.5b	(/.f64 (+.f64 (/.f64 1 (pow.f64 x 3/2)) (/.f64 -1 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))))
	31.3b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))) (fma.f64 (neg.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1))))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))))
	25.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 x 1) -1/2))
	25.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	31.4b	(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (/.f64 1 (cbrt.f64 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	31.3b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	61.6b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 x 1))) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))) (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (*.f64 1 1)))))))
	61.5b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 x 1))) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))) (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))))))
	61.4b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 x 1))) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))) (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))))))
	30.8b	(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 32353 to 26171 computations (19.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
✓	0.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	4.2b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series52.0ms (0.5%)

Counts

3 → 16

Calls

3 calls:

39.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
3.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite414.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

1631×	`*-un-lft-identity_binary64`
1558×	`times-frac_binary64`
946×	`add-sqr-sqrt_binary64`
514×	`add-cube-cbrt_binary64`
468×	`distribute-lft-out_binary64`

Counts

3 → 762

Calls

3 calls:

79.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
69.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

simplify769.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
594×	`times-frac_binary64`
422×	`div-sub_binary64`
388×	`fma-neg_binary64`
296×	`distribute-rgt-in_binary64`

Counts

778 → 568

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	302	32070
1	682	27791
2	1939	25611
3	4269	25601
4	4605	25601
5	4819	25601

prune962.0ms (10.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	615	2	617
Fresh	20	1	21
Picked	1	0	1
Done	0	0	0
Total	636	3	639

Error

5.8b

Counts

639 → 3

Alt Table

Status	Error	Program
	36.8b	(/.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (fma.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 -1 x) 1) (/.f64 -1 (pow.f64 x 5)))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
▶	22.1b	(/.f64 (-.f64 (.f64 1 (+.f64 1 x)) (.f64 x 1)) (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	25.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27842 to 22168 computations (20.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 (.f64 1 (+.f64 1 x)) (.f64 x 1)) (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	3.6b	(-.f64 (.f64 1 (+.f64 1 x)) (.f64 x 1))
✓	5.7b	(*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))

series75.0ms (0.8%)

Counts

3 → 12

Calls

3 calls:

59.0ms

(/.f64 (-.f64 (*.f64 1 (+.f64 1 x)) (*.f64 x 1)) (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))

15.0ms

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

1.0ms

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

rewrite67.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 74

Calls

3 calls:

31.0ms

(/.f64 (-.f64 (*.f64 1 (+.f64 1 x)) (*.f64 x 1)) (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))

25.0ms

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

6.0ms

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

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

811×	`distribute-rgt-in_binary64`
787×	`distribute-lft-in_binary64`
645×	`times-frac_binary64`
345×	`fma-def_binary64`
93×	`associate-l_binary64`

Counts

86 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2223
1	363	1643
2	1294	1637
3	5318	1637

prune237.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	151	7	158
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	153	8	161

Error

5.6b

Counts

161 → 8

Alt Table

Status	Error	Program
	6.0b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	6.1b	(.f64 (sqrt.f64 (/.f64 1 (.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))) (sqrt.f64 (/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))))
▶	6.0b	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	24.2b	(.f64 (/.f64 1 (.f64 (fma.f64 x x x) (+.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) 3) (pow.f64 (/.f64 1 (sqrt.f64 x)) 3)))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 (/.f64 1 (+.f64 1 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))))
	8.8b	(.f64 (/.f64 1 (.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	6.0b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
	25.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	22.2b	(/.f64 (-.f64 (.f64 1 (+.f64 1 x)) (.f64 x 1)) (.f64 (.f64 (fma.f64 x x x) (sqrt.f64 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))) (sqrt.f64 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))))

Compiler

Compiled 5868 to 3925 computations (33.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (+.f64 1 x)))
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	0.4b	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	5.7b	(*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))

series68.0ms (0.7%)

Counts

2 → 4

Calls

2 calls:

58.0ms	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
9.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 x)))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
18×	`sqrt-prod_binary64`
17×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`

Counts

2 → 68

Calls

2 calls:

26.0ms	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
4.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 x)))

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-neg_binary64`
463×	`associate-/l/_binary64`
421×	`associate-l_binary64`
411×	`distribute-rgt-in_binary64`
401×	`distribute-lft-in_binary64`

Counts

72 → 88

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1508
1	273	1334
2	820	1321
3	3066	1265
4	4710	1264
5	4994	1264

prune252.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	168	7	175

Error

0.0b

Counts

175 → 7

Alt Table

Status	Error	Program
✓	6.0b	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	0.4b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 x)))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 (/.f64 1 (+.f64 1 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))))
	0.4b	(/.f64 1 (.f64 (+.f64 1 x) (+.f64 (sqrt.f64 x) (.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 x)))))))
	6.0b	(/.f64 1 (.f64 (fma.f64 x x x) (+.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))))) (/.f64 1 (sqrt.f64 x)))))
	0.6b	(.f64 (sqrt.f64 (/.f64 1 (.f64 (+.f64 1 x) (+.f64 (sqrt.f64 x) (.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 x)))))))) (sqrt.f64 (/.f64 1 (.f64 (+.f64 1 x) (+.f64 (sqrt.f64 x) (*.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 x)))))))))
	6.0b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
	25.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 4485 to 2926 computations (34.8% saved)

regimes2.1s (22.1%)

Accuracy

Total 0.6b remaining (95.4%)

Threshold costs 0.6b (95.4%)

Counts

473 → 1

Compiler

Compiled 35524 to 29108 computations (18.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	17	26
2	16	26

end191.0ms (2%)

Compiler: Compiled 222 to 170 computations (23.4% saved)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17

Details

analyze1.0ms (0%)

sample1.3s (13.7%)

simplify12.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series48.0ms (0.5%)

rewrite231.0ms (2.4%)

simplify834.0ms (8.8%)

prune1.6s (17.2%)

localize14.0ms (0.2%)

series52.0ms (0.5%)

rewrite414.0ms (4.4%)

simplify769.0ms (8.1%)

prune962.0ms (10.2%)

localize16.0ms (0.2%)

series75.0ms (0.8%)

rewrite67.0ms (0.7%)

simplify57.0ms (0.6%)

prune237.0ms (2.5%)

localize12.0ms (0.1%)

series68.0ms (0.7%)

rewrite35.0ms (0.4%)

simplify94.0ms (1%)

prune252.0ms (2.7%)

regimes2.1s (22.1%)

simplify2.0ms (0%)

end191.0ms (2%)

Profiling

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17