Details

analyze1.0s (3.1%)

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
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)

sample1.4s (4.3%)

Results

1.1s	8256×	body	128	valid
266.0ms	2168×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify133.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
752×	`fma-neg_binary64`
239×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	33	11
3	64	11
4	125	11
5	238	11
6	414	11
7	791	11
8	1182	11
9	1373	11
10	1483	11
11	1532	11
12	1538	11
13	1543	11
14	1543	11
15	1458	11

prune3.0ms (0%)

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
▶	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

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

series19.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

19.0ms

(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)

simplify67.0ms (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

prune22.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Error

0.0b

Counts

33 → 5

Alt Table

Status	Error	Program
✓	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)))
	35.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
	5.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 538 to 160 computations (70.3% saved)

localize16.0ms (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)

series364.0ms (1.1%)

Counts

3 → 144

Calls

3 calls:

253.0ms

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

90.0ms

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

20.0ms

(*.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)))

rewrite21.0ms (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:

7.0ms

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

6.0ms

(*.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)))

1.0ms

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

simplify352.0ms (1%)

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

prune748.0ms (2.2%)

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
	35.2b	(*.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 (.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)))))
▶	3.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	35.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
	5.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 44997 to 18403 computations (59.1% saved)

localize10.0ms (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)

series26.9s (80%)

Counts

1 → 48

Calls

1 calls:

26.9s

(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

prune137.0ms (0.4%)

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
	35.2b	(*.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 (.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)))))
✓	3.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	35.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
	5.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 8558 to 4096 computations (52.1% saved)

localize13.0ms (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)

series87.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

86.0ms

(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))))

rewrite55.0ms (0.2%)

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:

54.0ms

(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))))

simplify96.0ms (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

prune1.3s (3.8%)

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
	35.2b	(*.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 (.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)))))
✓	3.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	35.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
	5.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 104054 to 37029 computations (64.4% saved)

regimes630.0ms (1.9%)

Accuracy

Total 0.8b remaining (97.3%)

Threshold costs 0.8b (97.3%)

Counts

68 → 3

Compiler

Compiled 11381 to 4193 computations (63.2% saved)

bsearch4.0ms (0%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
7×	`*-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	24	77
1	33	77
2	43	77
3	54	77
4	60	77
5	63	77
6	64	77
7	64	77

end82.0ms (0.2%)

Compiler: Compiled 248 to 100 computations (59.7% saved)

Details

analyze1.0s (3.1%)

sample1.4s (4.3%)

simplify133.0ms (0.4%)

prune3.0ms (0%)

localize6.0ms (0%)

series19.0ms (0.1%)

rewrite1.0ms (0%)

simplify67.0ms (0.2%)

prune22.0ms (0.1%)

localize16.0ms (0%)

series364.0ms (1.1%)

rewrite21.0ms (0.1%)

simplify352.0ms (1%)

prune748.0ms (2.2%)

localize10.0ms (0%)

series26.9s (80%)

rewrite3.0ms (0%)

simplify62.0ms (0.2%)

prune137.0ms (0.4%)

localize13.0ms (0%)

series87.0ms (0.3%)

rewrite55.0ms (0.2%)

simplify96.0ms (0.3%)

prune1.3s (3.8%)

regimes630.0ms (1.9%)

bsearch4.0ms (0%)

simplify5.0ms (0%)

end82.0ms (0.2%)

Profiling