Details

analyze1.4s (17.1%)

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
16.4%	83.4%	0.2%	9
21.4%	78.4%	0.2%	10
25.9%	73.3%	0.8%	11
28%	70.2%	1.9%	12
39.6%	55.8%	4.6%	13
43.9%	50.4%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample41.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
4.0ms	78×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify108.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
661×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	61	11
4	129	11
5	232	11
6	397	11
7	667	11
8	1062	11
9	1355	11
10	1480	11
11	1529	11
12	1535	11
13	1540	11
14	1540	11
15	1455	11

prune6.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	8.9b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
▶	8.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) t)
✓	8.1b	(fma.f64 y (/.f64 (-.f64 z x) t) x)

series60.0ms (0.8%)

Counts

2 → 76

Calls

2 calls:

39.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)
20.0ms	(/.f64 (-.f64 z x) t)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

10.0ms	(/.f64 (-.f64 z x) t)
1.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)

simplify109.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

704×	`distribute-rgt-in_binary64`
694×	`distribute-lft-in_binary64`
580×	`times-frac_binary64`
456×	`fma-def_binary64`
219×	`div-sub_binary64`

Counts

126 → 76

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	112	1693
1	247	1350
2	554	1350
3	1352	1350
4	4976	1350

prune90.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	73	5	78

Error

0.0b

Counts

78 → 5

Alt Table

Status	Error	Program
✓	8.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	35.6b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
	8.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
▶	2.2b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

Compiler

Compiled 1214 to 344 computations (71.7% saved)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series20.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

20.0ms

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

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
389×	`distribute-rgt-in_binary64`
386×	`distribute-lft-in_binary64`
294×	`times-frac_binary64`

Counts

58 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	87	635
2	197	623
3	473	623
4	2335	623
5	4674	623
6	5331	623

prune15.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	24	5	29

Error

0.0b

Counts

29 → 5

Alt Table

Status	Error	Program
✓	8.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	35.6b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
▶	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
	8.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
✓	2.2b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

Compiler

Compiled 431 to 135 computations (68.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
✓	0.6b	(cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))
	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series992.0ms (12.5%)

Counts

3 → 144

Calls

3 calls:

705.0ms

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

255.0ms

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

31.0ms

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

rewrite25.0ms (0.3%)

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:

8.0ms

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

7.0ms

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

1.0ms

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

simplify431.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

955×	`fma-def_binary64`
519×	`*-commutative_binary64`
218×	`+-commutative_binary64`
213×	`associate-r_binary64`
142×	`associate-+r+_binary64`

Counts

237 → 276

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1200	19267
1	4369	18981
2	5128	18981

prune1.2s (15%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	532	0	532
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	532	5	537

Error

0.0b

Counts

537 → 5

Alt Table

Status	Error	Program
✓	8.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	35.6b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
✓	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
▶	8.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
✓	2.2b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

Compiler

Compiled 43955 to 18294 computations (58.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y z) t) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
✓	7.7b	(/.f64 (*.f64 y x) t)
✓	8.0b	(/.f64 (*.f64 y z) t)

series90.0ms (1.1%)

Counts

4 → 24

Calls

4 calls:

29.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
27.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
18.0ms	(/.f64 (*.f64 y z) t)
16.0ms	(/.f64 (*.f64 y x) t)

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
28×	`prod-diff_binary64`
28×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`

Counts

4 → 126

Calls

4 calls:

17.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
10.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
7.0ms	(/.f64 (*.f64 y z) t)
6.0ms	(/.f64 (*.f64 y x) t)

simplify309.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

928×	`times-frac_binary64`
635×	`fma-def_binary64`
193×	`cancel-sign-sub-inv_binary64`
170×	`neg-mul-1_binary64`
162×	`distribute-rgt-neg-in_binary64`

Counts

150 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	3546
1	539	2223
2	1887	1903
3	4439	1903
4	4992	1903
5	4889	1903

prune171.0ms (2.2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	185	6	191

Error

Counts

191 → 6

Alt Table

Status	Error	Program
✓	8.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	35.6b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
✓	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
✓	8.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	36.3b	(-.f64 (fma.f64 (/.f64 y (sqrt.f64 t)) (/.f64 z (sqrt.f64 t)) x) (/.f64 (*.f64 y x) t))
✓	2.2b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

Compiler

Compiled 4392 to 798 computations (81.8% saved)

regimes1.3s (16.1%)

Accuracy

Total 2.1b remaining (99.3%)

Threshold costs 0b (0%)

Counts

72 → 6

Compiler

Compiled 7461 to 3808 computations (49% saved)

bsearch120.0ms (1.5%)

Steps

Iters	Range		Point
4	3.509282723391286e-87	1.234697245046296e-86	6.146152116507481e-87
8	8.026568213617949e-98	9.190181880310014e-95	1.1627240810470034e-97
4	1.3174670707205019e-152	1.9104397890161133e-152	1.7432692600882257e-152
7	-1.9641684264294804e-262	-2.3894953950451507e-264	-6.611843170999734e-264
7	-2.2244561483009195e-72	-4.8496365417548834e-82	-5.7190163307483135e-77

Compiler

Compiled 5 to 4 computations (20% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
10×	`*-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	135
1	58	135
2	77	135
3	87	135
4	93	135
5	94	135
6	94	135

end2.0ms (0%)

Compiler: Compiled 96 to 39 computations (59.4% saved)

sample1.3s (16.5%)

Algorithm

1×

intervals

Results

448.0ms	8000×	body	128	valid
114.0ms	2035×	body	128	invalid

Compiler

Compiled 231 to 106 computations (54.1% saved)

Details

analyze1.4s (17.1%)

sample41.0ms (0.5%)

simplify108.0ms (1.4%)

prune6.0ms (0.1%)

localize12.0ms (0.1%)

series60.0ms (0.8%)

rewrite15.0ms (0.2%)

simplify109.0ms (1.4%)

prune90.0ms (1.1%)

localize12.0ms (0.2%)

series20.0ms (0.2%)

rewrite1.0ms (0%)

simplify73.0ms (0.9%)

prune15.0ms (0.2%)

localize19.0ms (0.2%)

series992.0ms (12.5%)

rewrite25.0ms (0.3%)

simplify431.0ms (5.4%)

prune1.2s (15%)

localize18.0ms (0.2%)

series90.0ms (1.1%)

rewrite55.0ms (0.7%)

simplify309.0ms (3.9%)

prune171.0ms (2.2%)

regimes1.3s (16.1%)

bsearch120.0ms (1.5%)

simplify13.0ms (0.2%)

end2.0ms (0%)

sample1.3s (16.5%)

Profiling