Details

analyze1.3s (7.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.5s (8.5%)

Results

893.0ms	6948×	body	128	valid
160.0ms	474×	body	512	valid
157.0ms	390×	body	1024	valid
112.0ms	790×	body	128	invalid
82.0ms	384×	body	256	valid
26.0ms	60×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify129.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

prune3.0ms (0%)

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

9.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.6b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	16.9b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	4.2b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series60.0ms (0.3%)

Counts

2 → 96

Calls

2 calls:

41.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
19.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 t z) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

simplify112.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
644×	`fma-neg_binary64`
523×	`cancel-sign-sub-inv_binary64`
397×	`sub-neg_binary64`
195×	`div-sub_binary64`

Counts

160 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	4255
1	740	4157
2	2480	3550
3	4430	3531
4	5167	3531

prune130.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	132	7	139

Error

0.0b

Counts

139 → 7

Alt Table

Status	Error	Program
▶	11.6b	(*.f64 1 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))
	30.8b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	12.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
	26.4b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	28.2b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	37.3b	(fma.f64 y (-.f64 (fma.f64 (+.f64 1 (/.f64 a t)) (/.f64 z t) -1) (/.f64 a t)) (+.f64 x y))
	15.2b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 3688 to 1234 computations (66.5% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (-.f64 t z) (-.f64 a t))
	4.2b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

prune125.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	137	7	144

Error

0.0b

Counts

144 → 7

Alt Table

Status	Error	Program
✓	11.6b	(*.f64 1 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))
	30.8b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
▶	12.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
	26.4b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	28.2b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	37.3b	(fma.f64 y (-.f64 (fma.f64 (+.f64 1 (/.f64 a t)) (/.f64 z t) -1) (/.f64 a t)) (+.f64 x y))
	15.2b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 3943 to 1496 computations (62.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
✓	0.5b	(cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))
	4.2b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series9.3s (52.7%)

Counts

3 → 180

Calls

3 calls:

8.2s

(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))

1.1s

(cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))

51.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))

5.0ms

(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))

1.0ms

(cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))

simplify545.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

273 → 207

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5349	96726

prune2.0s (11.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	504	1	505
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	504	8	512

Error

0.0b

Counts

512 → 8

Alt Table

Status	Error	Program
✓	11.6b	(*.f64 1 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))
	30.8b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	36.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))))
✓	12.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
	26.4b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	28.2b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	37.3b	(fma.f64 y (-.f64 (fma.f64 (+.f64 1 (/.f64 a t)) (/.f64 z t) -1) (/.f64 a t)) (+.f64 x y))
▶	15.2b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 106228 to 57194 computations (46.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x)
✓	3.5b	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
✓	4.5b	(/.f64 (*.f64 y z) (-.f64 a t))
✓	11.4b	(/.f64 (*.f64 y t) (-.f64 a t))

series97.0ms (0.5%)

Counts

4 → 108

Calls

4 calls:

30.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
24.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x)
23.0ms	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
20.0ms	(/.f64 (*.f64 y t) (-.f64 a t))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
14×	`fma-def_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 103

Calls

4 calls:

9.0ms	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
7.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x)
5.0ms	(/.f64 (*.f64 y t) (-.f64 a t))
5.0ms	(/.f64 (*.f64 y z) (-.f64 a t))

simplify116.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
337×	`fma-neg_binary64`
314×	`distribute-rgt-in_binary64`
234×	`cancel-sign-sub-inv_binary64`
227×	`distribute-lft-in_binary64`

Counts

211 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	3951
1	721	3855
2	2505	3245
3	4746	3245
4	5005	3245

prune156.0ms (0.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	205	8	213

Error

0.0b

Counts

213 → 8

Alt Table

Status	Error	Program
✓	11.6b	(*.f64 1 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))
	30.8b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	15.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x)) (/.f64 y (/.f64 (-.f64 a t) z)))
✓	12.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
	26.4b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	37.3b	(fma.f64 y (-.f64 (fma.f64 (+.f64 1 (/.f64 a t)) (/.f64 z t) -1) (/.f64 a t)) (+.f64 x y))
✓	15.2b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
	42.3b	(-.f64 (/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 (/.f64 y (-.f64 a t)) t x) 3)) (fma.f64 y y (.f64 (fma.f64 (/.f64 y (-.f64 a t)) t x) (-.f64 (fma.f64 (/.f64 y (-.f64 a t)) t x) y)))) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 5769 to 1358 computations (76.5% saved)

regimes1.8s (10.1%)

Accuracy

Total 4.4b remaining (98.6%)

Threshold costs 0b (0%)

Counts

139 → 5

Compiler

Compiled 21396 to 11100 computations (48.1% saved)

bsearch5.0ms (0%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify25.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

71×	`distribute-rgt-neg-in_binary64`
60×	`cancel-sign-sub-inv_binary64`
50×	`distribute-lft-neg-in_binary64`
43×	`neg-sub0_binary64`
43×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	200
1	61	200
2	86	200
3	117	200
4	137	200
5	158	200
6	169	200
7	175	200
8	189	200
9	204	200
10	232	200
11	274	200
12	321	200
13	357	200
14	375	200
15	387	200
16	394	200
17	396	200
18	392	200

end124.0ms (0.7%)

Compiler: Compiled 511 to 187 computations (63.4% saved)

Iter	Nodes	Cost
0	40	200
1	61	200
2	86	200
3	117	200
4	137	200
5	158	200
6	169	200
7	175	200
8	189	200
9	204	200
10	232	200
11	274	200
12	321	200
13	357	200
14	375	200
15	387	200
16	394	200
17	396	200
18	392	200

Iter	Nodes	Cost
0	40	200
1	61	200
2	86	200
3	117	200
4	137	200
5	158	200
6	169	200
7	175	200
8	189	200
9	204	200
10	232	200
11	274	200
12	321	200
13	357	200
14	375	200
15	387	200
16	394	200
17	396	200
18	392	200

Details

analyze1.3s (7.4%)

sample1.5s (8.5%)

simplify129.0ms (0.7%)

prune3.0ms (0%)

localize8.0ms (0%)

series60.0ms (0.3%)

rewrite11.0ms (0.1%)

simplify112.0ms (0.6%)

prune130.0ms (0.7%)

localize10.0ms (0.1%)

prune125.0ms (0.7%)

localize11.0ms (0.1%)

series9.3s (52.7%)

rewrite22.0ms (0.1%)

simplify545.0ms (3.1%)

prune2.0s (11.5%)

localize11.0ms (0.1%)

series97.0ms (0.5%)

rewrite32.0ms (0.2%)

simplify116.0ms (0.7%)

prune156.0ms (0.9%)

regimes1.8s (10.1%)

bsearch5.0ms (0%)

simplify25.0ms (0.1%)

end124.0ms (0.7%)

Profiling

Iter	Nodes	Cost
0	40	200
1	61	200
2	86	200
3	117	200
4	137	200
5	158	200
6	169	200
7	175	200
8	189	200
9	204	200
10	232	200
11	274	200
12	321	200
13	357	200
14	375	200
15	387	200
16	394	200
17	396	200
18	392	200