Details

analyze2.0s (17.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample2.0s (17%)

Results

1.3s	8253×	body	128	valid
676.0ms	4529×	body	128	invalid
1.0ms	2×	body	256	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 83 to 59 computations (28.9% saved)

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

494×	`fma-neg_binary64`
474×	`distribute-neg-in_binary64`
463×	`associate--l-_binary64`
362×	`associate--r-_binary64`
354×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	49	27
2	141	25
3	466	25
4	1615	25
5	3794	25
6	4547	25
7	4966	25

prune4.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

Compiler

Compiled 93 to 60 computations (35.5% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))
✓	0.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

series43.0ms (0.4%)

Counts

2 → 132

Calls

2 calls:

28.0ms	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
15.0ms	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))

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	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
0.0ms	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))

simplify106.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

482×	`associate--l+_binary64`
479×	`associate--r+_binary64`
436×	`sub-neg_binary64`
415×	`associate-+l+_binary64`
273×	`associate-l_binary64`

Counts

152 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	3199
1	275	3115
2	832	2962
3	2890	2960
4	4883	2960
5	5007	2960

prune73.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Error

0.0b

Counts

75 → 4

Alt Table

Status	Error	Program
	12.2b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
▶	0.0b	(-.f64 (+.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x)))) (+.f64 (.f64 y z) (+.f64 (.f64 a t) (*.f64 2 b))))
	1.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))
	32.5b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (sqrt.f64 (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))

Compiler

Compiled 1662 to 836 computations (49.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 z (+.f64 (*.f64 t b) x))
✓	0.0b	(+.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))))
✓	0.0b	(+.f64 (.f64 y z) (+.f64 (.f64 a t) (*.f64 2 b)))
✓	0.0b	(-.f64 (+.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x)))) (+.f64 (.f64 y z) (+.f64 (.f64 a t) (*.f64 2 b))))

series67.0ms (0.6%)

Counts

4 → 135

Calls

4 calls:

31.0ms	(-.f64 (+.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x)))) (+.f64 (.f64 y z) (+.f64 (.f64 a t) (*.f64 2 b))))
16.0ms	(+.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))))
13.0ms	(+.f64 (.f64 y z) (+.f64 (.f64 a t) (*.f64 2 b)))
7.0ms	(+.f64 z (+.f64 (*.f64 t b) x))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`add-log-exp_binary64`
61×	`sum-log_binary64`
17×	`*-un-lft-identity_binary64`
15×	`diff-log_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

4 → 103

Calls

4 calls:

17.0ms	(-.f64 (+.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x)))) (+.f64 (.f64 y z) (+.f64 (.f64 a t) (*.f64 2 b))))
7.0ms	(+.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))))
4.0ms	(+.f64 (.f64 y z) (+.f64 (.f64 a t) (*.f64 2 b)))
4.0ms	(+.f64 z (+.f64 (*.f64 t b) x))

simplify139.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

484×	`times-frac_binary64`
470×	`fma-neg_binary64`
276×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`
257×	`sub-neg_binary64`

Counts

238 → 224

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	233	5147
1	711	4944
2	3333	4818
3	4868	4814
4	5052	4814

prune184.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	223	5	228

Error

Counts

228 → 5

Alt Table

Status	Error	Program
	12.2b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
✓	0.0b	(-.f64 (+.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x)))) (+.f64 (.f64 y z) (+.f64 (.f64 a t) (*.f64 2 b))))
	48.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 y b) 3) (pow.f64 (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))) 3)) (+.f64 (.f64 (.f64 y b) (.f64 y b)) (-.f64 (.f64 (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x)))) (.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))))))) (+.f64 (.f64 y z) (+.f64 (.f64 a t) (.f64 2 b))))
▶	1.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))
	32.5b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (sqrt.f64 (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))

Compiler

Compiled 8349 to 2396 computations (71.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))))
✓	0.6b	(cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

series2.7s (23.3%)

Counts

4 → 252

Calls

4 calls:

2.3s	(*.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))))
357.0ms	(cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
29.0ms	(fma.f64 (-.f64 (+.f64 y t) 2) b (.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))
17.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
15×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))))
4.0ms	(*.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))))
1.0ms	(cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
0.0ms	(fma.f64 (-.f64 (+.f64 y t) 2) b (.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))

simplify479.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

355 → 235

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5787	223338361872

prune1.9s (15.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	381	0	381
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	381	5	386

Error

Counts

386 → 5

Alt Table

Status	Error	Program
▶	12.2b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
✓	0.0b	(-.f64 (+.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x)))) (+.f64 (.f64 y z) (+.f64 (.f64 a t) (*.f64 2 b))))
	48.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 y b) 3) (pow.f64 (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))) 3)) (+.f64 (.f64 (.f64 y b) (.f64 y b)) (-.f64 (.f64 (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x)))) (.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))))))) (+.f64 (.f64 y z) (+.f64 (.f64 a t) (.f64 2 b))))
✓	1.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))
	32.5b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (sqrt.f64 (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))

Compiler

Compiled 90953 to 64202 computations (29.4% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (-.f64 b z) (*.f64 b -2))

series8.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(fma.f64 y (-.f64 b z) (*.f64 b -2))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (-.f64 b z) (*.f64 b -2))

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

865×	`neg-mul-1_binary64`
571×	`distribute-rgt-neg-out_binary64`
472×	`distribute-lft-neg-out_binary64`
374×	`unsub-neg_binary64`
359×	`distribute-neg-out_binary64`

Counts

46 → 28

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	598
1	75	494
2	161	494
3	451	494
4	2018	494
5	3929	494
6	5425	494

prune29.0ms (0.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	28	5	33

Error

Counts

33 → 5

Alt Table

Status	Error	Program
✓	12.2b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
✓	0.0b	(-.f64 (+.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x)))) (+.f64 (.f64 y z) (+.f64 (.f64 a t) (*.f64 2 b))))
	48.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 y b) 3) (pow.f64 (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))) 3)) (+.f64 (.f64 (.f64 y b) (.f64 y b)) (-.f64 (.f64 (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x)))) (.f64 (.f64 y b) (+.f64 a (+.f64 z (+.f64 (.f64 t b) x))))))) (+.f64 (.f64 y z) (+.f64 (.f64 a t) (.f64 2 b))))
✓	1.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (cbrt.f64 (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))
	32.5b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))) (sqrt.f64 (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))))

Compiler

Compiled 708 to 325 computations (54.1% saved)

regimes1.6s (13.8%)

Accuracy

Total 0.0b remaining (52.6%)

Threshold costs 0.0b (52.6%)

Counts

165 → 1

Compiler

Compiled 31918 to 20907 computations (34.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
9×	`*-commutative_binary64`
9×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	28	29
2	38	29
3	58	29
4	71	29
5	81	29
6	85	29
7	84	29

end119.0ms (1%)

Compiler: Compiled 276 to 154 computations (44.2% saved)

Details

analyze2.0s (17.2%)

sample2.0s (17%)

simplify61.0ms (0.5%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series43.0ms (0.4%)

rewrite1.0ms (0%)

simplify106.0ms (0.9%)

prune73.0ms (0.6%)

localize16.0ms (0.1%)

series67.0ms (0.6%)

rewrite43.0ms (0.4%)

simplify139.0ms (1.2%)

prune184.0ms (1.6%)

localize15.0ms (0.1%)

series2.7s (23.3%)

rewrite21.0ms (0.2%)

simplify479.0ms (4.1%)

prune1.9s (15.9%)

localize9.0ms (0.1%)

series8.0ms (0.1%)

rewrite1.0ms (0%)

simplify58.0ms (0.5%)

prune29.0ms (0.3%)

regimes1.6s (13.8%)

simplify3.0ms (0%)

end119.0ms (1%)

Profiling