Details

analyze908.0ms (9.7%)

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
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
22.8%	77%	0.2%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.3s (13.9%)

Results

898.0ms	8256×	body	128	valid
232.0ms	2203×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
730×	`fma-neg_binary64`
228×	`cancel-sign-sub-inv_binary64`
138×	`distribute-rgt-in_binary64`
97×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	11
2	31	11
3	72	11
4	146	11
5	255	11
6	409	11
7	668	11
8	1099	11
9	1352	11
10	1478	11
11	1525	11
12	1531	11
13	1536	11
14	1536	11
15	1451	11

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

2.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.5b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series24.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

23.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

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 (-.f64 y x) (/.f64 z t) x)

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-neg-out_binary64`
515×	`distribute-lft-neg-out_binary64`
375×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
270×	`times-frac_binary64`

Counts

58 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	88	635
2	194	623
3	469	623
4	2305	623
5	4632	623
6	5238	623

prune22.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	4	32

Error

0.0b

Counts

32 → 4

Alt Table

Status	Error	Program
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	35.5b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
▶	5.6b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
	6.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 472 to 140 computations (70.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
✓	0.0b	(/.f64 (-.f64 y x) t)
✓	5.5b	(*.f64 z (/.f64 (-.f64 y x) t))

series51.0ms (0.5%)

Counts

3 → 124

Calls

3 calls:

23.0ms	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
19.0ms	(*.f64 z (/.f64 (-.f64 y x) t))
9.0ms	(/.f64 (-.f64 y x) t)

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

3 → 94

Calls

3 calls:

7.0ms	(*.f64 z (/.f64 (-.f64 y x) t))
5.0ms	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
4.0ms	(/.f64 (-.f64 y x) t)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Rules

409×	`distribute-rgt-in_binary64`
396×	`distribute-lft-in_binary64`
346×	`associate-*l/_binary64`
330×	`associate-*r/_binary64`
276×	`fma-def_binary64`

Counts

218 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	2779
1	425	2436
2	1259	2427
3	4230	2427
4	4978	2427

prune90.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	133	6	139

Error

Counts

139 → 6

Alt Table

Status	Error	Program
	6.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
	5.7b	(+.f64 (*.f64 z (/.f64 1 (/.f64 t (-.f64 y x)))) x)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	5.6b	(+.f64 (*.f64 z (-.f64 (/.f64 y t) (/.f64 x t))) x)
	33.3b	(+.f64 (.f64 (.f64 z (/.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (sqrt.f64 t))) (/.f64 (cbrt.f64 (-.f64 y x)) (sqrt.f64 t))) x)
	6.0b	(+.f64 (.f64 (.f64 z (*.f64 (cbrt.f64 (/.f64 (-.f64 y x) t)) (cbrt.f64 (/.f64 (-.f64 y x) t)))) (cbrt.f64 (/.f64 (-.f64 y x) t))) x)

Compiler

Compiled 2335 to 635 computations (72.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 z (-.f64 (/.f64 y t) (/.f64 x t))) x)
✓	0.7b	(-.f64 (/.f64 y t) (/.f64 x t))
✓	5.5b	(*.f64 z (-.f64 (/.f64 y t) (/.f64 x t)))

series57.0ms (0.6%)

Counts

3 → 114

Calls

3 calls:

24.0ms	(*.f64 z (-.f64 (/.f64 y t) (/.f64 x t)))
21.0ms	(+.f64 (*.f64 z (-.f64 (/.f64 y t) (/.f64 x t))) x)
11.0ms	(-.f64 (/.f64 y t) (/.f64 x t))

rewrite301.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

1244×	`times-frac_binary64`
987×	`add-sqr-sqrt_binary64`
977×	`*-un-lft-identity_binary64`
961×	`add-cube-cbrt_binary64`
845×	`prod-diff_binary64`

Counts

3 → 998

Calls

3 calls:

36.0ms	(+.f64 (*.f64 z (-.f64 (/.f64 y t) (/.f64 x t))) x)
22.0ms	(*.f64 z (-.f64 (/.f64 y t) (/.f64 x t)))
14.0ms	(-.f64 (/.f64 y t) (/.f64 x t))

simplify728.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

657×	`distribute-rgt-in_binary64`
419×	`fma-neg_binary64`
410×	`associate-l_binary64`
410×	`unsub-neg_binary64`
398×	`*-commutative_binary64`

Counts

1112 → 1454

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	781	33333
1	1327	22680
2	2795	16424
3	4739	16424
4	4812	16424

prune3.1s (33%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1454	0	1454
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	1454	6	1460

Error

Counts

1460 → 6

Alt Table

Status	Error	Program
	6.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
▶	5.7b	(+.f64 (*.f64 z (/.f64 1 (/.f64 t (-.f64 y x)))) x)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	5.6b	(+.f64 (*.f64 z (-.f64 (/.f64 y t) (/.f64 x t))) x)
	33.3b	(+.f64 (.f64 (.f64 z (/.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (sqrt.f64 t))) (/.f64 (cbrt.f64 (-.f64 y x)) (sqrt.f64 t))) x)
	6.0b	(+.f64 (.f64 (.f64 z (*.f64 (cbrt.f64 (/.f64 (-.f64 y x) t)) (cbrt.f64 (/.f64 (-.f64 y x) t)))) (cbrt.f64 (/.f64 (-.f64 y x) t))) x)

Compiler

Compiled 58413 to 12941 computations (77.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 y x))
✓	0.0b	(+.f64 (*.f64 z (/.f64 1 (/.f64 t (-.f64 y x)))) x)
✓	0.8b	(/.f64 1 (/.f64 t (-.f64 y x)))
✓	5.5b	(*.f64 z (/.f64 1 (/.f64 t (-.f64 y x))))

series69.0ms (0.7%)

Counts

4 → 156

Calls

4 calls:

23.0ms	(+.f64 (*.f64 z (/.f64 1 (/.f64 t (-.f64 y x)))) x)
18.0ms	(*.f64 z (/.f64 1 (/.f64 t (-.f64 y x))))
17.0ms	(/.f64 t (-.f64 y x))
12.0ms	(/.f64 1 (/.f64 t (-.f64 y x)))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

252×	`times-frac_binary64`
186×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
122×	`add-cube-cbrt_binary64`
68×	`associate-r_binary64`

Counts

4 → 262

Calls

4 calls:

17.0ms	(*.f64 z (/.f64 1 (/.f64 t (-.f64 y x))))
10.0ms	(+.f64 (*.f64 z (/.f64 1 (/.f64 t (-.f64 y x)))) x)
7.0ms	(/.f64 1 (/.f64 t (-.f64 y x)))
4.0ms	(/.f64 t (-.f64 y x))

simplify139.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

543×	`times-frac_binary64`
477×	`distribute-rgt-in_binary64`
475×	`fma-def_binary64`
455×	`distribute-lft-in_binary64`
130×	`associate-l_binary64`

Counts

418 → 390

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	6343
1	620	5676
2	1926	5487
3	5178	5487

prune256.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	389	1	390
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	390	6	396

Error

Counts

396 → 6

Alt Table

Status	Error	Program
	6.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	5.7b	(+.f64 (*.f64 z (/.f64 1 (/.f64 t (-.f64 y x)))) x)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	5.6b	(+.f64 (*.f64 z (-.f64 (/.f64 y t) (/.f64 x t))) x)
	6.0b	(+.f64 (.f64 (.f64 z (*.f64 (cbrt.f64 (/.f64 (-.f64 y x) t)) (cbrt.f64 (/.f64 (-.f64 y x) t)))) (cbrt.f64 (/.f64 (-.f64 y x) t))) x)
	33.8b	(+.f64 (.f64 (.f64 z (/.f64 1 (/.f64 1 (sqrt.f64 (-.f64 y x))))) (/.f64 1 (/.f64 t (sqrt.f64 (-.f64 y x))))) x)

Compiler

Compiled 8081 to 2928 computations (63.8% saved)

regimes1.9s (20.2%)

Accuracy

Total 1.7b remaining (98.7%)

Threshold costs 0b (0%)

Counts

143 → 4

Compiler

Compiled 16673 to 10188 computations (38.9% saved)

bsearch4.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	82
1	36	82
2	44	82
3	48	82
4	50	82
5	49	82

end85.0ms (0.9%)

Compiler: Compiled 234 to 117 computations (50% saved)

Details

analyze908.0ms (9.7%)

sample1.3s (13.9%)

simplify67.0ms (0.7%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series24.0ms (0.3%)

rewrite1.0ms (0%)

simplify66.0ms (0.7%)

prune22.0ms (0.2%)

localize6.0ms (0.1%)

series51.0ms (0.5%)

rewrite23.0ms (0.2%)

simplify90.0ms (1%)

prune90.0ms (1%)

localize7.0ms (0.1%)

series57.0ms (0.6%)

rewrite301.0ms (3.2%)

simplify728.0ms (7.8%)

prune3.1s (33%)

localize16.0ms (0.2%)

series69.0ms (0.7%)

rewrite63.0ms (0.7%)

simplify139.0ms (1.5%)

prune256.0ms (2.7%)

regimes1.9s (20.2%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end85.0ms (0.9%)

Profiling