Details

analyze8.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample1.2s (40.8%)

Results

1.1s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 62 to 47 computations (24.2% saved)

simplify77.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

750×	`div-sub_binary64`
748×	`fma-neg_binary64`
599×	`fma-def_binary64`
502×	`associate-/l*_binary64`
423×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	37	29
2	82	27
3	201	27
4	526	27
5	991	25
6	1614	25
7	3273	25
8	3653	25
9	4694	25
10	4942	25

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
▶	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 113 to 86 computations (23.9% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
✓	0.0b	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
✓	0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
✓	0.1b	(.f64 3 (.f64 v v))

series32.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

15.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
10.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
3.0ms	(.f64 3 (.f64 v v))

rewrite68.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
26×	`associate-l_binary64`
25×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
23×	`add-cbrt-cube_binary64`

Counts

4 → 143

Calls

4 calls:

31.0ms	(.f64 3 (.f64 v v))
11.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
9.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))

simplify130.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

674×	`cancel-sign-sub-inv_binary64`
427×	`times-frac_binary64`
389×	`associate-l_binary64`
374×	`associate-r_binary64`
274×	`fma-neg_binary64`

Counts

191 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	5429
1	967	5084
2	3434	5016
3	5413	5016

prune242.0ms (8.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	251	3	254

Error

Counts

254 → 3

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))
▶	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 8015 to 6003 computations (25.1% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 v (*.f64 v -3) 1))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))

series30.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

14.0ms

(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))))

11.0ms

(*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))

5.0ms

(sqrt.f64 (fma.f64 v (*.f64 v -3) 1))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`pow1_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
16×	`distribute-lft-in_binary64`
16×	`distribute-rgt-in_binary64`

Counts

3 → 76

Calls

3 calls:

8.0ms

(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))))

6.0ms

(*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))

1.0ms

(sqrt.f64 (fma.f64 v (*.f64 v -3) 1))

simplify120.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-def_binary64`
672×	`fma-neg_binary64`
569×	`cancel-sign-sub-inv_binary64`
256×	`associate-r_binary64`
230×	`sub-neg_binary64`

Counts

112 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	233	3324
1	644	3084
2	2350	2985
3	4364	2978
4	4988	2978

prune143.0ms (5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	147	2	149

Error

Counts

149 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
▶	1.0b	(.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))) 3)))

Status

Error

Program

✓

0.0b

(*.f64 (*.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (-.f64 1 (*.f64 v v)))

▶

1.0b

(*.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))) 3)))

Compiler

Compiled 4206 to 3459 computations (17.8% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))
✓	0.0b	(.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))) 3)))
✓	0.0b	(pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))) 3)
✓	1.0b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))) 3))

series130.0ms (4.6%)

Counts

3 → 36

Calls

3 calls:

62.0ms

(*.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))) 3)))

43.0ms

(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))) 3))

24.0ms

(pow.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))) 3)

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`cbrt-prod_binary64`
19×	`add-sqr-sqrt_binary64`
11×	`associate-r_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`

Counts

3 → 82

Calls

3 calls:

7.0ms

(*.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))) 3)))

6.0ms

(pow.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))) 3)

2.0ms

(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))) 3))

simplify132.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

678×	`fma-neg_binary64`
324×	`sub-neg_binary64`
310×	`associate-r_binary64`
230×	`associate-l_binary64`
223×	`fma-def_binary64`

Counts

118 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	274	4419
1	782	4102
2	3305	4066
3	4882	4066
4	5056	4066

prune247.0ms (8.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	231	2	233

Error

Counts

233 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
✓	1.0b	(.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))) 3)))

Status

Error

Program

✓

0.0b

(*.f64 (*.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (-.f64 1 (*.f64 v v)))

✓

1.0b

(*.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))) 3)))

Compiler

Compiled 7853 to 6608 computations (15.9% saved)

regimes176.0ms (6.2%)

Accuracy

Total 0.0b remaining (49.3%)

Threshold costs 0.0b (49.3%)

Counts

60 → 1

Compiler

Compiled 3370 to 2781 computations (17.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	21	25
2	20	25

end65.0ms (2.3%)

Compiler: Compiled 77 to 60 computations (22.1% saved)

Details

analyze8.0ms (0.3%)

sample1.2s (40.8%)

simplify77.0ms (2.7%)

prune4.0ms (0.1%)

localize12.0ms (0.4%)

series32.0ms (1.1%)

rewrite68.0ms (2.4%)

simplify130.0ms (4.6%)

prune242.0ms (8.5%)

localize11.0ms (0.4%)

series30.0ms (1.1%)

rewrite22.0ms (0.8%)

simplify120.0ms (4.2%)

prune143.0ms (5%)

localize14.0ms (0.5%)

series130.0ms (4.6%)

rewrite20.0ms (0.7%)

simplify132.0ms (4.7%)

prune247.0ms (8.7%)

regimes176.0ms (6.2%)

simplify2.0ms (0.1%)

end65.0ms (2.3%)

Profiling