Details

analyze882.0ms (14.2%)

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)

sample1.2s (19.7%)

Results

894.0ms	8256×	body	128	valid
214.0ms	2105×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify73.0ms (1.2%)

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 (0.1%)

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
▶	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	7.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series15.0ms (0.2%)

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)

simplify71.0ms (1.1%)

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

prune23.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Error

0.0b

Counts

33 → 5

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	7.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
▶	2.3b	(.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)))
	42.8b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 z t) (-.f64 y x) x) 3))
	37.9b	(*.f64 z (/.f64 (-.f64 y x) t))

Compiler

Compiled 510 to 156 computations (69.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))
	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series501.0ms (8%)

Counts

3 → 144

Calls

3 calls:

350.0ms

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

127.0ms

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

23.0ms

(*.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)))

rewrite20.0ms (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:

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)))

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))

simplify259.0ms (4.2%)

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

prune579.0ms (9.3%)

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
	34.4b	(.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 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	42.8b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 z t) (-.f64 y x) x) 3))
▶	2.3b	(.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)))))
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	7.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
	37.9b	(*.f64 z (/.f64 (-.f64 y x) t))

Compiler

Compiled 45029 to 18405 computations (59.1% saved)

localize12.0ms (0.2%)

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))))
	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series190.0ms (3.1%)

Counts

1 → 48

Calls

1 calls:

190.0ms

(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 (0.1%)

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))))

simplify135.0ms (2.2%)

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 (20.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	961	0	961
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	961	6	967

Error

0.0b

Counts

967 → 6

Alt Table

Status	Error	Program
	34.4b	(.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 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	42.8b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 z t) (-.f64 y x) x) 3))
✓	2.3b	(.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)))))
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	7.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
	37.9b	(*.f64 z (/.f64 (-.f64 y x) t))

Compiler

Compiled 104154 to 37068 computations (64.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y x) z)
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
✓	7.4b	(/.f64 (*.f64 (-.f64 y x) z) t)

series44.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

20.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
18.0ms	(/.f64 (*.f64 (-.f64 y x) z) t)
6.0ms	(*.f64 (-.f64 y x) z)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 66

Calls

3 calls:

6.0ms	(/.f64 (*.f64 (-.f64 y x) z) t)
4.0ms	(*.f64 (-.f64 y x) z)
3.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

546×	`times-frac_binary64`
512×	`associate-/l*_binary64`
379×	`div-sub_binary64`
319×	`distribute-rgt-in_binary64`
318×	`associate-*l/_binary64`

Counts

198 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	2596
1	365	2080
2	1123	1980
3	4594	1980
4	5596	1980

prune85.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	3	0	3
Picked	1	0	1
Done	0	2	2
Total	127	5	132

Error

Counts

132 → 5

Alt Table

Status	Error	Program
✓	2.3b	(.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)))))
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	0.9b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
	7.3b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 (-.f64 y x) z))))
	33.1b	(+.f64 x (*.f64 (/.f64 (-.f64 y x) (sqrt.f64 t)) (/.f64 z (sqrt.f64 t))))

Compiler

Compiled 1914 to 521 computations (72.8% saved)

regimes643.0ms (10.3%)

Accuracy

Total 2.1b remaining (98.7%)

Threshold costs 0b (0%)

Counts

128 → 1

Compiler

Compiled 19376 to 7803 computations (59.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	17	13
3	19	13
4	20	13
5	20	13

end61.0ms (1%)

Compiler: Compiled 137 to 63 computations (54% saved)

Details

analyze882.0ms (14.2%)

sample1.2s (19.7%)

simplify73.0ms (1.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series15.0ms (0.2%)

rewrite1.0ms (0%)

simplify71.0ms (1.1%)

prune23.0ms (0.4%)

localize9.0ms (0.1%)

series501.0ms (8%)

rewrite20.0ms (0.3%)

simplify259.0ms (4.2%)

prune579.0ms (9.3%)

localize12.0ms (0.2%)

series190.0ms (3.1%)

rewrite6.0ms (0.1%)

simplify135.0ms (2.2%)

prune1.3s (20.5%)

localize6.0ms (0.1%)

series44.0ms (0.7%)

rewrite16.0ms (0.3%)

simplify82.0ms (1.3%)

prune85.0ms (1.4%)

regimes643.0ms (10.3%)

simplify2.0ms (0%)

end61.0ms (1%)

Profiling