Details

analyze2.0ms (0%)

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)

sample1.8s (23.2%)

Results

744.0ms	6086×	body	128	valid
398.0ms	1077×	body	1024	valid
212.0ms	664×	body	512	valid
71.0ms	329×	body	256	valid
50.0ms	100×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify210.0ms (2.8%)

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 → 2

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

Error

16.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series69.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

49.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
20.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
18×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

10.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify98.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

960×	`times-frac_binary64`
218×	`+-commutative_binary64`
206×	`fma-def_binary64`
194×	`fma-neg_binary64`
193×	`associate-+r+_binary64`

Counts

112 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	3790
1	962	3664
2	3486	3620
3	4984	3620

prune131.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	139	4	143

Error

0.0b

Counts

143 → 4

Alt Table

Status	Error	Program
	44.7b	(/.f64 (+.f64 beta 1) alpha)
▶	16.7b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	16.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	46.4b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 4357 to 2679 computations (38.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
	1.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	1.4b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

series101.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

61.0ms	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
39.0ms	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`exp-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`log-prod_binary64`

Counts

2 → 32

Calls

2 calls:

2.0ms	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
1.0ms	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

simplify104.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

363×	`sub-neg_binary64`
288×	`times-frac_binary64`
253×	`fma-def_binary64`
251×	`+-commutative_binary64`
247×	`associate-+r+_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	4045
1	1105	3894
2	4579	3852
3	5169	3852

prune288.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	254	5	259

Error

0.0b

Counts

259 → 5

Alt Table

Status	Error	Program
▶	17.2b	(.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (log.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))))
	44.7b	(/.f64 (+.f64 beta 1) alpha)
✓	16.7b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	16.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	46.4b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 9419 to 6271 computations (33.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	1.2b	(log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
	1.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series1.2s (15.5%)

Counts

3 → 72

Calls

3 calls:

464.0ms

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

457.0ms

(log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))

249.0ms

(cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

3 → 71

Calls

3 calls:

6.0ms

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

1.0ms

(log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))

1.0ms

(cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

simplify393.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

381×	`*-commutative_binary64`
332×	`+-commutative_binary64`
294×	`fma-def_binary64`
280×	`associate-+r+_binary64`
168×	`associate-*r/_binary64`

Counts

143 → 179

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1146	27367
1	4239	26174
2	4970	26174

prune1.1s (15.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	438	1	439
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	439	5	444

Error

0.0b

Counts

444 → 5

Alt Table

Status	Error	Program
	44.7b	(/.f64 (+.f64 beta 1) alpha)
✓	16.7b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
▶	17.2b	(.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (exp.f64 (.f64 2 (log.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2))))))
✓	16.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	46.4b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 57183 to 41099 computations (28.1% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f64 (*.f64 2 (log.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))))
	1.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	1.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)
✓	2.6b	(log.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))

series883.0ms (11.7%)

Counts

3 → 72

Calls

3 calls:

532.0ms

(exp.f64 (*.f64 2 (log.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))))

316.0ms

(log.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))

35.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`log-prod_binary64`
12×	`exp-sum_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`cbrt-prod_binary64`

Counts

3 → 52

Calls

3 calls:

2.0ms

(exp.f64 (*.f64 2 (log.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))))

1.0ms

(log.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))

0.0ms

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

simplify195.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

322×	`+-commutative_binary64`
300×	`*-commutative_binary64`
280×	`fma-def_binary64`
260×	`associate-+r+_binary64`
177×	`associate-*r/_binary64`

Counts

124 → 170

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1023	13573
1	3681	12907
2	4960	12907

prune471.0ms (6.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	216	5	221

Error

0.0b

Counts

221 → 5

Alt Table

Status	Error	Program
	44.7b	(/.f64 (+.f64 beta 1) alpha)
✓	16.7b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	17.2b	(.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (exp.f64 (.f64 2 (log.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2))))))
✓	16.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	46.4b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 21990 to 16092 computations (26.8% saved)

regimes330.0ms (4.4%)

Accuracy

Total 0.0b remaining (28.7%)

Threshold costs 0.0b (28.7%)

Counts

39 → 2

Compiler

Compiled 4951 to 3662 computations (26% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	78
1	37	78
2	48	78
3	61	78
4	67	78
5	69	78
6	67	78

end125.0ms (1.7%)

Compiler: Compiled 239 to 146 computations (38.9% saved)

Details

analyze2.0ms (0%)

sample1.8s (23.2%)

simplify210.0ms (2.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series69.0ms (0.9%)

rewrite15.0ms (0.2%)

simplify98.0ms (1.3%)

prune131.0ms (1.7%)

localize11.0ms (0.2%)

series101.0ms (1.3%)

rewrite4.0ms (0.1%)

simplify104.0ms (1.4%)

prune288.0ms (3.8%)

localize14.0ms (0.2%)

series1.2s (15.5%)

rewrite13.0ms (0.2%)

simplify393.0ms (5.2%)

prune1.1s (15.1%)

localize20.0ms (0.3%)

series883.0ms (11.7%)

rewrite8.0ms (0.1%)

simplify195.0ms (2.6%)

prune471.0ms (6.2%)

regimes330.0ms (4.4%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end125.0ms (1.7%)

Profiling