Details

analyze911.0ms (2.8%)

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
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 (4%)

Results

904.0ms	8256×	body	128	valid
239.0ms	2168×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify65.0ms (0.2%)

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%)

Local error

Found 1 expressions with local error:

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

series15.0ms (0%)

Counts

1 → 48

Calls

1 calls:

15.0ms

(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)

simplify65.0ms (0.2%)

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

prune19.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	5	32

Error

0.0b

Counts

32 → 5

Alt Table

Status	Error	Program
	35.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	35.2b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
▶	3.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	5.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 538 to 160 computations (70.3% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
	2.5b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series356.0ms (1.1%)

Counts

3 → 144

Calls

3 calls:

252.0ms

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

82.0ms

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

21.0ms

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

rewrite23.0ms (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:

11.0ms

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

4.0ms

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

1.0ms

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

simplify301.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
540×	`*-commutative_binary64`
218×	`+-commutative_binary64`
210×	`associate-r_binary64`
141×	`associate-+r+_binary64`

Counts

237 → 277

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1216	19471
1	4389	19186
2	5141	19186

prune617.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	552	2	554
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	553	6	559

Error

0.0b

Counts

559 → 6

Alt Table

Status	Error	Program
	35.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	3.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
	3.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
	35.2b	(*.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 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 44997 to 18403 computations (59.1% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
	2.5b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series27.0s (81.6%)

Counts

1 → 48

Calls

1 calls:

27.0s

(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 32

Calls

1 calls:

2.0ms

(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)

simplify62.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

677×	`times-frac_binary64`
647×	`associate-/l*_binary64`
194×	`unswap-sqr_binary64`
150×	`fma-def_binary64`
115×	`associate-/r/_binary64`

Counts

80 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	2768
1	395	2560
2	1370	2197
3	4983	2197

prune160.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	198	6	204

Error

0.0b

Counts

204 → 6

Alt Table

Status	Error	Program
	35.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	3.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
▶	3.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
	35.2b	(*.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 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 8558 to 4096 computations (52.1% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	0.5b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
✓	0.5b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	2.5b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series85.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

85.0ms

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

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`rem-cbrt-cube_binary64`
1×	`pow3_binary64`
1×	`cbrt-prod_binary64`

Counts

1 → 12

Calls

1 calls:

5.0ms

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

simplify94.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

593×	`times-frac_binary64`
370×	`associate-/r*_binary64`
344×	`associate-/l*_binary64`
296×	`fma-def_binary64`
195×	`associate-*r/_binary64`

Counts

60 → 96

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	446	5390
1	1530	5195
2	5105	5195

prune1.2s (3.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	961	0	961
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	961	6	967

Error

0.0b

Counts

967 → 6

Alt Table

Status	Error	Program
	35.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	3.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
✓	3.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
	35.2b	(*.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 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 104054 to 37029 computations (64.4% saved)

regimes670.0ms (2%)

Accuracy

Total 1.8b remaining (98.8%)

Threshold costs 0b (0%)

Counts

68 → 3

Compiler

Compiled 13658 to 5032 computations (63.2% saved)

bsearch31.0ms (0.1%)

Steps

Iters	Range		Point
2	1.0502114923970225e-39	1.3455129705198305e-38	1.9957900418829807e-39
9	-1.4225115268085278e+117	-4.977180743871039e+111	-3.0549464306960693e+114

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	53
1	28	53
2	38	53
3	49	53
4	55	53
5	58	53
6	59	53
7	59	53

end80.0ms (0.2%)

Compiler: Compiled 216 to 94 computations (56.5% saved)

Details

analyze911.0ms (2.8%)

sample1.3s (4%)

simplify65.0ms (0.2%)

prune3.0ms (0%)

localize5.0ms (0%)

series15.0ms (0%)

rewrite1.0ms (0%)

simplify65.0ms (0.2%)

prune19.0ms (0.1%)

localize9.0ms (0%)

series356.0ms (1.1%)

rewrite23.0ms (0.1%)

simplify301.0ms (0.9%)

prune617.0ms (1.9%)

localize8.0ms (0%)

series27.0s (81.6%)

rewrite3.0ms (0%)

simplify62.0ms (0.2%)

prune160.0ms (0.5%)

localize12.0ms (0%)

series85.0ms (0.3%)

rewrite6.0ms (0%)

simplify94.0ms (0.3%)

prune1.2s (3.5%)

regimes670.0ms (2%)

bsearch31.0ms (0.1%)

simplify6.0ms (0%)

end80.0ms (0.2%)

Profiling