Details

analyze919.0ms (16.8%)

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
24%	75.2%	0.8%	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)

sample1.4s (25.8%)

Results

1.0s	8256×	body	128	valid
225.0ms	2067×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify67.0ms (1.2%)

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

prune3.0ms (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
▶	6.4b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	7.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) t)
✓	6.1b	(fma.f64 y (/.f64 (-.f64 z x) t) x)

series29.0ms (0.5%)

Counts

2 → 76

Calls

2 calls:

20.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)
9.0ms	(/.f64 (-.f64 z x) t)

rewrite7.0ms (0.1%)

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:

4.0ms	(/.f64 (-.f64 z x) t)
0.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)

simplify66.0ms (1.2%)

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

prune58.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	71	7	78

Error

Counts

78 → 7

Alt Table

Status	Error	Program
	7.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
	2.8b	(.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)))
	6.9b	(fma.f64 y (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 t))) x)
	6.4b	(fma.f64 y (/.f64 (/.f64 (-.f64 z x) 1) t) x)
	34.6b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z x) t)) (sqrt.f64 (/.f64 (-.f64 z x) t))) x)
▶	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	6.9b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)

Compiler

Compiled 1304 to 395 computations (69.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.5b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series18.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

18.0ms

(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)

simplify66.0ms (1.2%)

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

prune18.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	24	7	31

Error

Counts

31 → 7

Alt Table

Status	Error	Program
	7.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
▶	2.8b	(.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)))
	6.9b	(fma.f64 y (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 t))) x)
	6.4b	(fma.f64 y (/.f64 (/.f64 (-.f64 z x) 1) t) x)
	34.6b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z x) t)) (sqrt.f64 (/.f64 (-.f64 z x) t))) x)
✓	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	6.9b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)

Compiler

Compiled 521 to 186 computations (64.3% saved)

localize9.0ms (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))
	1.5b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series553.0ms (10.1%)

Counts

3 → 144

Calls

3 calls:

388.0ms

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

146.0ms

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

18.0ms

(*.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)))

rewrite21.0ms (0.4%)

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)))

4.0ms

(*.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))

simplify287.0ms (5.3%)

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

prune898.0ms (16.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	532	0	532
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	532	7	539

Error

Counts

539 → 7

Alt Table

Status	Error	Program
	7.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	2.8b	(.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)))
	6.9b	(fma.f64 y (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 t))) x)
▶	6.4b	(fma.f64 y (/.f64 (/.f64 (-.f64 z x) 1) t) x)
	34.6b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z x) t)) (sqrt.f64 (/.f64 (-.f64 z x) t))) x)
✓	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	6.9b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)

Compiler

Compiled 44045 to 18345 computations (58.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (-.f64 z x) 1) t)
✓	6.1b	(fma.f64 y (/.f64 (/.f64 (-.f64 z x) 1) t) x)

series57.0ms (1%)

Counts

2 → 84

Calls

2 calls:

47.0ms	(fma.f64 y (/.f64 (/.f64 (-.f64 z x) 1) t) x)
10.0ms	(/.f64 (/.f64 (-.f64 z x) 1) t)

rewrite58.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`times-frac_binary64`
82×	`*-un-lft-identity_binary64`
82×	`add-sqr-sqrt_binary64`
58×	`add-cube-cbrt_binary64`
19×	`associate-/l*_binary64`

Counts

2 → 108

Calls

2 calls:

7.0ms	(/.f64 (/.f64 (-.f64 z x) 1) t)
0.0ms	(fma.f64 y (/.f64 (/.f64 (-.f64 z x) 1) t) x)

simplify117.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-def_binary64`
379×	`neg-mul-1_binary64`
372×	`fma-neg_binary64`
317×	`associate-/r*_binary64`
294×	`associate-/r/_binary64`

Counts

192 → 161

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	148	2750
1	249	2392
2	626	2392
3	1679	2392
4	3890	2392
5	4966	2392

prune121.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	161	7	168

Error

Counts

168 → 7

Alt Table

Status	Error	Program
	7.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	2.8b	(.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)))
	6.9b	(fma.f64 y (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 t))) x)
✓	6.4b	(fma.f64 y (/.f64 (/.f64 (-.f64 z x) 1) t) x)
	34.6b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z x) t)) (sqrt.f64 (/.f64 (-.f64 z x) t))) x)
✓	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	6.9b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)

Compiler

Compiled 3043 to 1220 computations (59.9% saved)

regimes518.0ms (9.5%)

Accuracy

Total 1.4b remaining (99%)

Threshold costs 0b (0%)

Counts

87 → 3

Compiler

Compiled 9306 to 5163 computations (44.5% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	71
1	29	71
2	33	71
3	35	71
4	36	71
5	35	71

end129.0ms (2.4%)

Compiler: Compiled 242 to 101 computations (58.3% saved)

Details

analyze919.0ms (16.8%)

sample1.4s (25.8%)

simplify67.0ms (1.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series29.0ms (0.5%)

rewrite7.0ms (0.1%)

simplify66.0ms (1.2%)

prune58.0ms (1.1%)

localize6.0ms (0.1%)

series18.0ms (0.3%)

rewrite1.0ms (0%)

simplify66.0ms (1.2%)

prune18.0ms (0.3%)

localize9.0ms (0.2%)

series553.0ms (10.1%)

rewrite21.0ms (0.4%)

simplify287.0ms (5.3%)

prune898.0ms (16.5%)

localize7.0ms (0.1%)

series57.0ms (1%)

rewrite58.0ms (1.1%)

simplify117.0ms (2.1%)

prune121.0ms (2.2%)

regimes518.0ms (9.5%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end129.0ms (2.4%)

Profiling