Details

analyze934.0ms (19.5%)

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)

sample1.5s (30.3%)

Results

1.0s	8256×	body	128	valid
263.0ms	2095×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify68.0ms (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

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
▶	5.1b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	5.5b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) t)
✓	4.8b	(fma.f64 y (/.f64 (-.f64 z x) t) x)

series30.0ms (0.6%)

Counts

2 → 76

Calls

2 calls:

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

rewrite10.0ms (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:

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

simplify61.0ms (1.3%)

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

prune46.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	71	5	76
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	73	5	78

Error

0.0b

Counts

78 → 5

Alt Table

Status	Error	Program
	34.1b	(fma.f64 y (/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 t (sqrt.f64 (-.f64 z x)))) x)
▶	2.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	5.5b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	3.5b	(.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)))
	5.1b	(+.f64 (*.f64 y (/.f64 (-.f64 z x) t)) x)

Compiler

Compiled 1218 to 353 computations (71% saved)

localize18.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series16.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

16.0ms

(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)

simplify70.0ms (1.5%)

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

prune11.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	24	5	29

Error

0.0b

Counts

29 → 5

Alt Table

Status	Error	Program
	34.1b	(fma.f64 y (/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 t (sqrt.f64 (-.f64 z x)))) x)
✓	2.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	5.5b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
▶	3.5b	(.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)))
	5.1b	(+.f64 (*.f64 y (/.f64 (-.f64 z x) t)) x)

Compiler

Compiled 435 to 144 computations (66.9% saved)

localize10.0ms (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)))
✓	0.5b	(*.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))
	2.2b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series366.0ms (7.6%)

Counts

3 → 144

Calls

3 calls:

260.0ms

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

83.0ms

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

22.0ms

(*.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)))

rewrite20.0ms (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:

6.0ms

(*.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)))

6.0ms

(*.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))

simplify279.0ms (5.8%)

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

prune593.0ms (12.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	531	1	532
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	531	6	537

Error

Counts

537 → 6

Alt Table

Status	Error	Program
	34.1b	(fma.f64 y (/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 t (sqrt.f64 (-.f64 z x)))) x)
✓	2.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	5.5b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	35.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (cbrt.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))))) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
✓	3.5b	(.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)))
▶	5.1b	(+.f64 (*.f64 y (/.f64 (-.f64 z x) t)) x)

Compiler

Compiled 44029 to 18329 computations (58.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 y (/.f64 (-.f64 z x) t)) x)
	0.0b	(/.f64 (-.f64 z x) t)
✓	5.7b	(*.f64 y (/.f64 (-.f64 z x) t))

series46.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

24.0ms	(+.f64 (*.f64 y (/.f64 (-.f64 z x) t)) x)
22.0ms	(*.f64 y (/.f64 (-.f64 z x) t))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
18×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 54

Calls

2 calls:

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

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

769×	`times-frac_binary64`
457×	`distribute-rgt-in_binary64`
439×	`distribute-lft-in_binary64`
352×	`associate-*r/_binary64`
340×	`associate-*l/_binary64`

Counts

150 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	2030
1	336	1719
2	1147	1710
3	4232	1710
4	5164	1710

prune76.0ms (1.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	136	6	142

Error

Counts

142 → 6

Alt Table

Status	Error	Program
	34.1b	(fma.f64 y (/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 t (sqrt.f64 (-.f64 z x)))) x)
✓	2.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	35.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (cbrt.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))))) (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
✓	3.5b	(.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)))
✓	5.1b	(+.f64 (*.f64 y (/.f64 (-.f64 z x) t)) x)
	5.5b	(+.f64 (/.f64 (-.f64 (.f64 y z) (.f64 y x)) t) x)

Compiler

Compiled 2263 to 584 computations (74.2% saved)

regimes464.0ms (9.7%)

Accuracy

Total 3.0b remaining (99.4%)

Threshold costs 0b (0%)

Counts

50 → 3

Compiler

Compiled 4236 to 2378 computations (43.9% saved)

bsearch35.0ms (0.7%)

Steps

Iters	Range		Point
6	1.6484468046764002e-294	1.7234734380376712e-293	1.1791014341897874e-293
1	-1.638484109646957e+147	-5.697151056999243e+146	-9.793361331116636e+146

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
7×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	61
1	40	61
2	52	61
3	58	61
4	61	61
5	61	61

end85.0ms (1.8%)

Compiler: Compiled 216 to 104 computations (51.9% saved)

Details

analyze934.0ms (19.5%)

sample1.5s (30.3%)

simplify68.0ms (1.4%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series30.0ms (0.6%)

rewrite10.0ms (0.2%)

simplify61.0ms (1.3%)

prune46.0ms (1%)

localize18.0ms (0.4%)

series16.0ms (0.3%)

rewrite1.0ms (0%)

simplify70.0ms (1.5%)

prune11.0ms (0.2%)

localize10.0ms (0.2%)

series366.0ms (7.6%)

rewrite20.0ms (0.4%)

simplify279.0ms (5.8%)

prune593.0ms (12.4%)

localize6.0ms (0.1%)

series46.0ms (0.9%)

rewrite15.0ms (0.3%)

simplify73.0ms (1.5%)

prune76.0ms (1.6%)

regimes464.0ms (9.7%)

bsearch35.0ms (0.7%)

simplify4.0ms (0.1%)

end85.0ms (1.8%)

Profiling