Details

analyze278.0ms (4.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample34.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	191×	body	128	valid
5.0ms	31×	body	1024	valid
5.0ms	256×	pre	128	true
3.0ms	17×	body	512	valid
2.0ms	13×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify224.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

890×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l*_binary64`
388×	`distribute-rgt-neg-in_binary64`
379×	`neg-mul-1_binary64`

Counts

1 → 1

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	64	19
4	108	19
5	215	17
6	353	17
7	603	17
8	1141	17
9	2484	17
10	3195	17
11	3981	17
12	4235	17
13	4399	17
14	4503	17
15	4531	17
16	4533	17
17	4768	17
18	4708	17
19	4930	17
20	4826	17

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

15.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	15.9b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
2.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

rewrite104.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

15.6b

Rules

20×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

2 → 87

Calls

2 calls:

20.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
11.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 1714 to 921 computations (46.3% saved)

series121.0ms (2.1%)

Error

0.1b

Counts

2 → 42

Calls

2 calls:

55.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
40.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 2630 to 2056 computations (21.8% saved)

simplify125.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

319×	`cancel-sign-sub-inv_binary64`
285×	`sub-neg_binary64`
244×	`fma-neg_binary64`
191×	`fma-def_binary64`
185×	`+-commutative_binary64`

Counts

129 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	290	3419
1	911	3285
2	3338	3221
3	4977	3220
4	5018	3220

prune107.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Error

0.0b

Counts

83 → 4

Alt Table

Status	Error	Program
	46.5b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
▶	15.9b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
	24.9b	(/.f64 (fma.f64 (pow.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 3) -1/8 1/8) (+.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 alpha beta)) 6) (pow.f64 (cbrt.f64 (+.f64 beta (+.f64 2 alpha))) 6)) 1/4 1/4) (*.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 1/4)))
	16.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))

Compiler

Compiled 1981 to 1194 computations (39.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha)))
2.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)

rewrite104.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

20×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

2 → 87

Calls

2 calls:

31.0ms	(/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha)))
10.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)

Compiler

Compiled 1714 to 1059 computations (38.2% saved)

series133.0ms (2.3%)

Error

0.0b

Counts

2 → 42

Calls

2 calls:

56.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
55.0ms	(/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha)))

Compiler

Compiled 2630 to 2056 computations (21.8% saved)

simplify126.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

329×	`cancel-sign-sub-inv_binary64`
290×	`sub-neg_binary64`
212×	`fma-neg_binary64`
202×	`fma-def_binary64`
186×	`distribute-neg-in_binary64`

Counts

129 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	287	3428
1	909	3298
2	3337	3230
3	4969	3229
4	4976	3229

prune37.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Error

0.0b

Counts

57 → 4

Alt Table

Status	Error	Program
	46.5b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	15.9b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
	24.9b	(/.f64 (fma.f64 (pow.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 3) -1/8 1/8) (+.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 alpha beta)) 6) (pow.f64 (cbrt.f64 (+.f64 beta (+.f64 2 alpha))) 6)) 1/4 1/4) (*.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 1/4)))
▶	16.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))

Compiler

Compiled 1432 to 872 computations (39.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))
2.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
2.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
2.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)

rewrite183.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`add-cube-cbrt_binary64`
18×	`pow1/3_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`fma-udef_binary64`
14×	`pow1_binary64`

Counts

4 → 141

Calls

4 calls:

16.0ms	(*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))
12.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
11.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
11.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)

Compiler

Compiled 5430 to 3536 computations (34.9% saved)

series577.0ms (9.8%)

Error

0.0b

Counts

4 → 80

Calls

4 calls:

264.0ms	(*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))
68.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
68.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
65.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)

Compiler

Compiled 13274 to 10295 computations (22.4% saved)

simplify149.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

396×	`associate-/r*_binary64`
381×	`times-frac_binary64`
363×	`fma-def_binary64`
292×	`associate-/l*_binary64`
212×	`associate-r_binary64`

Counts

221 → 108

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	454	9438
1	1508	8404
2	4982	8404

prune126.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	108	4	112

Error

0.0b

Counts

112 → 4

Alt Table

Status	Error	Program
	46.5b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	15.9b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
	24.9b	(/.f64 (fma.f64 (pow.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 3) -1/8 1/8) (+.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 alpha beta)) 6) (pow.f64 (cbrt.f64 (+.f64 beta (+.f64 2 alpha))) 6)) 1/4 1/4) (*.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 1/4)))
▶	15.9b	(*.f64 (log.f64 (exp.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2) 2/3))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))

Compiler

Compiled 6303 to 3948 computations (37.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2) 2/3)
1.9b	(log.f64 (exp.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2) 2/3)))
2.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
2.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)

rewrite241.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

27×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`add-cbrt-cube_binary64`
12×	`log1p-expm1-u_binary64`

Counts

4 → 137

Calls

4 calls:

52.0ms	(pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2) 2/3)
10.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
10.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
10.0ms	(log.f64 (exp.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2) 2/3)))

Compiler

Compiled 4551 to 3127 computations (31.3% saved)

series684.0ms (11.7%)

Error

0.0b

Counts

4 → 76

Calls

4 calls:

288.0ms	(log.f64 (exp.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2) 2/3)))
165.0ms	(pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2) 2/3)
64.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
64.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)

Compiler

Compiled 12413 to 9857 computations (20.6% saved)

simplify206.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

457×	`fma-def_binary64`
364×	`associate-/r*_binary64`
361×	`times-frac_binary64`
257×	`associate-/l*_binary64`
202×	`associate-*r/_binary64`

Counts

213 → 110

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	504	9569
1	1594	8426
2	4982	8426
3	5105	8426

prune142.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	110	4	114

Error

0.0b

Counts

114 → 4

Alt Table

Status	Error	Program
	46.5b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	15.9b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
	24.9b	(/.f64 (fma.f64 (pow.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 3) -1/8 1/8) (+.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 alpha beta)) 6) (pow.f64 (cbrt.f64 (+.f64 beta (+.f64 2 alpha))) 6)) 1/4 1/4) (*.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 1/4)))
	15.9b	(.f64 (log.f64 (exp.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2) 2/3))) (cbrt.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 3) -1/8 1/8) (+.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) (.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 1/4) 1/4) (*.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) 1/4)))))

Compiler

Compiled 5954 to 3751 computations (37% saved)

regimes946.0ms (16.1%)

Accuracy

Total 0.1b remaining (59.9%)

Threshold costs 0.1b (59.9%)

Compiler

Compiled 17860 to 12761 computations (28.5% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	108
1	54	108
2	68	108
3	83	108
4	90	108
5	92	108
6	90	108

end1.0ms (0%)

Compiler: Compiled 74 to 46 computations (37.8% saved)

sample1.2s (19.7%)

Algorithm

1×

intervals

Results

271.0ms	5944×	body	128	valid
167.0ms	1007×	body	1024	valid
149.0ms	8000×	pre	128	true
75.0ms	604×	body	512	valid
29.0ms	340×	body	256	valid
21.0ms	105×	body	2048	valid

Compiler

Compiled 258 to 167 computations (35.3% saved)

Details

analyze278.0ms (4.7%)

sample34.0ms (0.6%)

simplify224.0ms (3.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite104.0ms (1.8%)

series121.0ms (2.1%)

simplify125.0ms (2.1%)

prune107.0ms (1.8%)

localize7.0ms (0.1%)

rewrite104.0ms (1.8%)

series133.0ms (2.3%)

simplify126.0ms (2.1%)

prune37.0ms (0.6%)

localize13.0ms (0.2%)

rewrite183.0ms (3.1%)

series577.0ms (9.8%)

simplify149.0ms (2.5%)

prune126.0ms (2.1%)

localize16.0ms (0.3%)

rewrite241.0ms (4.1%)

series684.0ms (11.7%)

simplify206.0ms (3.5%)

prune142.0ms (2.4%)

regimes946.0ms (16.1%)

bsearch6.0ms (0.1%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample1.2s (19.7%)

Profiling