Details

analyze1.2s (18.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample4.0s (60%)

Results

2.4s	4110×	body	2048	valid
954.0ms	2103×	body	1024	valid
338.0ms	1025×	body	512	valid
117.0ms	502×	body	256	valid
68.0ms	516×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

686×	`div-sub_binary64`
546×	`sub-neg_binary64`
397×	`neg-mul-1_binary64`
344×	`neg-sub0_binary64`
311×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	31	19
2	72	17
3	203	17
4	532	17
5	1340	17
6	2710	17
7	3748	17
8	4643	17
9	4981	17

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

Compiler

Compiled 53 to 36 computations (32.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 v (*.f64 v -5) 1)
✓	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 v (*.f64 v -5) 1)
2.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
0.0ms	(fma.f64 v (*.f64 v -5) 1)

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Rules

702×	`distribute-rgt-in_binary64`
335×	`distribute-rgt-out_binary64`
251×	`neg-mul-1_binary64`
239×	`exp-prod_binary64`
236×	`associate-l_binary64`

Counts

44 → 30

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	686
1	56	616
2	93	615
3	272	615
4	1239	615
5	4506	615
6	4933	615

prune24.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	3	31

Error

0.4b

Counts

31 → 3

Alt Table

Status	Error	Program
▶	1.4b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.0b	(.f64 (.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
✓	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

Compiler

Compiled 656 to 466 computations (29% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 v (*.f64 v -5) 1)
	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
✓	1.0b	(sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	1.0b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

series9.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

7.0ms

(sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))

2.0ms

(*.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms

(*.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

1.0ms

(sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))

simplify123.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
446×	`unswap-sqr_binary64`
308×	`sqr-pow_binary64`
292×	`associate-+l+_binary64`
259×	`associate-/l*_binary64`

Counts

92 → 79

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	61	2100
1	83	1942
2	188	1864
3	398	1738
4	739	1738
5	1373	1738
6	2606	1724
7	4626	1724
8	5184	1724

prune133.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	158	3	161

Error

0.4b

Counts

161 → 3

Alt Table

Status	Error	Program
✓	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
	3.3b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
▶	1.9b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))

Compiler

Compiled 5442 to 3937 computations (27.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))
✓	1.0b	(sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1))))
	1.0b	(sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	2.2b	(acos.f64 (/.f64 1 (fma.f64 v v -1)))

series18.0ms (0.3%)

Counts

3 → 12

Calls

3 calls:

13.0ms

(*.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))

4.0ms

(sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1))))

2.0ms

(acos.f64 (/.f64 1 (fma.f64 v v -1)))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`

Counts

3 → 58

Calls

3 calls:

5.0ms

(*.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))

1.0ms

(sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1))))

1.0ms

(acos.f64 (/.f64 1 (fma.f64 v v -1)))

simplify148.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

380×	`fma-def_binary64`
359×	`unswap-sqr_binary64`
354×	`log-div_binary64`
273×	`associate-l_binary64`
230×	`cube-div_binary64`

Counts

70 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	2074
1	107	1988
2	229	1964
3	301	1964
4	457	1964
5	779	1964
6	1061	1964
7	2597	1964
8	3722	1964
9	4838	1964
10	4971	1964

prune84.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	94	4	98

Error

0.4b

Counts

98 → 4

Alt Table

Status	Error	Program
✓	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
	3.3b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
▶	3.2b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))))
✓	1.9b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))

Compiler

Compiled 3299 to 2459 computations (25.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))))
	1.0b	(sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1))))
	1.0b	(sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
	2.2b	(acos.f64 (/.f64 1 (fma.f64 v v -1)))

series11.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

11.0ms

(*.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
6×	`associate-l_binary64`
6×	`cbrt-unprod_binary64`
6×	`add-cbrt-cube_binary64`

Counts

1 → 26

Calls

1 calls:

13.0ms

(*.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))))

simplify111.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-def_binary64`
468×	`log-div_binary64`
377×	`associate-l_binary64`
346×	`associate-/l/_binary64`
341×	`unswap-sqr_binary64`

Counts

38 → 37

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	63	1396
1	107	1284
2	284	1252
3	663	1252
4	906	1239
5	1444	1239
6	1714	1239
7	2915	1239
8	4360	1239
9	5373	1239

prune154.0ms (2.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	136	5	141

Error

0.4b

Counts

141 → 5

Alt Table

Status	Error	Program
✓	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
	3.3b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
✓	1.9b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))
	4.0b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))))
	3.2b	(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 1 (fma.f64 v v -1)))))))))

Compiler

Compiled 7152 to 5514 computations (22.9% saved)

regimes196.0ms (3%)

Accuracy

Total 0.0b remaining (1.3%)

Threshold costs 0.0b (1.3%)

Counts

43 → 1

Compiler

Compiled 5614 to 4152 computations (26% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`distribute-lft-neg-in_binary64`
3×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	22	21
2	29	21
3	36	21
4	41	21
5	44	21
6	45	21
7	42	21

end179.0ms (2.7%)

Compiler: Compiled 277 to 205 computations (26% saved)

Details

analyze1.2s (18.5%)

sample4.0s (60%)

simplify73.0ms (1.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify68.0ms (1%)

prune24.0ms (0.4%)

localize9.0ms (0.1%)

series9.0ms (0.1%)

rewrite12.0ms (0.2%)

simplify123.0ms (1.9%)

prune133.0ms (2%)

localize13.0ms (0.2%)

series18.0ms (0.3%)

rewrite10.0ms (0.2%)

simplify148.0ms (2.2%)

prune84.0ms (1.3%)

localize16.0ms (0.2%)

series11.0ms (0.2%)

rewrite19.0ms (0.3%)

simplify111.0ms (1.7%)

prune154.0ms (2.3%)

regimes196.0ms (3%)

simplify3.0ms (0.1%)

end179.0ms (2.7%)

Profiling