Details

analyze374.0ms (2.4%)

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
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
74.9%	25%	0.2%	11
74.9%	25%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.5s (9.9%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify92.0ms (0.6%)

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

prune5.0ms (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

2.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series37.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

37.0ms

(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:

1.0ms

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

simplify104.0ms (0.7%)

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

prune26.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	4	32

Error

0.0b

Counts

32 → 4

Alt Table

Status	Error	Program
	29.2b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
	6.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	3.2b	(.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)))

Compiler

Compiled 492 to 142 computations (71.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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)))
	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	14.9b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))

series928.0ms (6%)

Counts

3 → 144

Calls

3 calls:

751.0ms

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

142.0ms

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

33.0ms

(*.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)))

rewrite43.0ms (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:

12.0ms

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

12.0ms

(*.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))

simplify519.0ms (3.3%)

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

prune1.6s (10.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	552	2	554
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	552	6	558

Error

0.0b

Counts

558 → 6

Alt Table

Status	Error	Program
✓	3.2b	(.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)))
▶	3.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
	29.2b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
	6.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
	24.7b	(.f64 (cbrt.f64 (.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 45022 to 18399 computations (59.1% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	14.9b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))

series798.0ms (5.1%)

Counts

2 → 96

Calls

2 calls:

572.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
225.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`

Counts

2 → 72

Calls

2 calls:

7.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

simplify421.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

916×	`fma-def_binary64`
521×	`*-commutative_binary64`
206×	`+-commutative_binary64`
199×	`associate-r_binary64`
140×	`associate-+r+_binary64`

Counts

168 → 234

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1209	19310
1	4255	19016
2	4988	19016

prune2.7s (17.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1036	1	1037
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1036	7	1043

Error

0.0b

Counts

1043 → 7

Alt Table

Status	Error	Program
▶	3.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.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 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))) (.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
	24.7b	(.f64 (cbrt.f64 (.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	3.2b	(.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)))
✓	3.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
	29.2b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
	6.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 110122 to 36227 computations (67.1% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	7.2b	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	14.9b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))

series657.0ms (4.2%)

Counts

2 → 96

Calls

2 calls:

465.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
191.0ms	(cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`cbrt-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
2.0ms	(cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))

simplify423.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

923×	`fma-def_binary64`
508×	`*-commutative_binary64`
208×	`+-commutative_binary64`
195×	`associate-r_binary64`
140×	`associate-+r+_binary64`

Counts

126 → 189

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1185	17613
1	4221	17283
2	4992	17283

prune3.6s (23.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1485	0	1485
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	1485	7	1492

Error

0.0b

Counts

1492 → 7

Alt Table

Status	Error	Program
✓	3.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.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 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))) (.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
	24.7b	(.f64 (cbrt.f64 (.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	3.2b	(.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)))
✓	3.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
	29.2b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
	6.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 229479 to 57182 computations (75.1% saved)

regimes1.3s (8.1%)

Accuracy

Total 1.4b remaining (98.9%)

Threshold costs 0b (0%)

Counts

83 → 3

Compiler

Compiled 29812 to 8839 computations (70.4% saved)

bsearch48.0ms (0.3%)

Steps

Iters	Range		Point
6	5.221281205288879e-187	6.442595614309442e-186	1.397538728800338e-186
6	-3.6433792469596574e-78	-6.991912478747801e-79	-7.49627756986184e-79

Compiler

Compiled 5 to 4 computations (20% saved)

simplify8.0ms (0.1%)

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	44
1	31	44
2	41	44
3	52	44
4	58	44
5	61	44
6	62	44
7	62	44

end197.0ms (1.3%)

Compiler: Compiled 333 to 117 computations (64.9% saved)

Details

analyze374.0ms (2.4%)

sample1.5s (9.9%)

simplify92.0ms (0.6%)

prune5.0ms (0%)

localize12.0ms (0.1%)

series37.0ms (0.2%)

rewrite1.0ms (0%)

simplify104.0ms (0.7%)

prune26.0ms (0.2%)

localize11.0ms (0.1%)

series928.0ms (6%)

rewrite43.0ms (0.3%)

simplify519.0ms (3.3%)

prune1.6s (10.4%)

localize21.0ms (0.1%)

series798.0ms (5.1%)

rewrite16.0ms (0.1%)

simplify421.0ms (2.7%)

prune2.7s (17.5%)

localize21.0ms (0.1%)

series657.0ms (4.2%)

rewrite6.0ms (0%)

simplify423.0ms (2.7%)

prune3.6s (23.4%)

regimes1.3s (8.1%)

bsearch48.0ms (0.3%)

simplify8.0ms (0.1%)

end197.0ms (1.3%)

Profiling