Details

analyze910.0ms (14.5%)

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
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.6s (25.1%)

Results

983.0ms	8256×	body	128	valid
370.0ms	3250×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	72	17
3	227	17
4	512	17
5	1044	17
6	1436	17
7	1492	17
8	1573	17
9	1615	17
10	1631	17
11	1631	17
12	1550	17

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

7.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.3b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))

Compiler

Compiled 63 to 37 computations (41.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
✓	0.0b	(-.f64 (*.f64 z z) t)
✓	6.9b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

series59.0ms (0.9%)

Counts

3 → 108

Calls

3 calls:

34.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
21.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
4.0ms	(-.f64 (*.f64 z z) t)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`cancel-sign-sub-inv_binary64`
16×	`prod-diff_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`associate--r+_binary64`
14×	`distribute-lft-in_binary64`

Counts

3 → 88

Calls

3 calls:

8.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
4.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
3.0ms	(-.f64 (*.f64 z z) t)

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
380×	`distribute-rgt-in_binary64`
359×	`distribute-lft-in_binary64`
305×	`exp-prod_binary64`
256×	`cancel-sign-sub-inv_binary64`

Counts

196 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	3113
1	410	2801
2	1537	2665
3	4564	2665
4	4917	2665

prune133.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	151	6	157
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	7	158

Error

2.9b

Counts

158 → 7

Alt Table

Status	Error	Program
	32.6b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (+.f64 z (sqrt.f64 t))) (-.f64 z (sqrt.f64 t))))
	39.5b	(.f64 y (.f64 4 t))
▶	26.4b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))
	42.9b	(-.f64 (.f64 x x) (/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 (.f64 z z) 3) (pow.f64 t 3))) (+.f64 (.f64 (.f64 z z) (.f64 z z)) (+.f64 (.f64 t t) (.f64 (.f64 z z) t)))))
	42.3b	(pow.f64 x 2)
	27.3b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (/.f64 (-.f64 (pow.f64 z 4) (.f64 t t)) (fma.f64 z z t))))
✓	7.3b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))

Compiler

Compiled 3500 to 1349 computations (61.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))
✓	0.1b	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
✓	0.2b	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
✓	6.8b	(sqrt.f64 (-.f64 (*.f64 z z) t))

series116.0ms (1.8%)

Counts

4 → 128

Calls

4 calls:

45.0ms	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
34.0ms	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))
21.0ms	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
15.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
16×	`sqrt-div_binary64`
14×	`associate-r_binary64`

Counts

4 → 95

Calls

4 calls:

14.0ms	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
7.0ms	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
4.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
3.0ms	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))

simplify124.0ms (2%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-def_binary64`
586×	`times-frac_binary64`
376×	`associate-l_binary64`
326×	`cancel-sign-sub-inv_binary64`
290×	`fma-neg_binary64`

Counts

223 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	4374
1	715	4019
2	2410	3852
3	4789	3852
4	4909	3852

prune163.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	262	3	265
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	266	6	272

Error

2.9b

Counts

272 → 6

Alt Table

Status	Error	Program
	26.5b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) t)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) t)))))
✓	26.4b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))
	32.6b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (+.f64 z (sqrt.f64 t))) (-.f64 z (sqrt.f64 t))))
▶	20.1b	(fma.f64 4 (.f64 t y) (.f64 x x))
	42.9b	(-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 (pow.f64 z 6) (pow.f64 t 3)) (*.f64 4 y)) (fma.f64 t (fma.f64 z z t) (pow.f64 z 4))))
✓	7.3b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))

Compiler

Compiled 7751 to 2562 computations (66.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (.f64 t y) (.f64 x x))

series14.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

14.0ms

(fma.f64 4 (*.f64 t y) (*.f64 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 4 (*.f64 t y) (*.f64 x x))

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

942×	`fma-def_binary64`
536×	`*-commutative_binary64`
517×	`distribute-rgt-out_binary64`
478×	`distribute-rgt-in_binary64`
472×	`distribute-lft-in_binary64`

Counts

46 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	511
1	33	488
2	69	488
3	194	488
4	736	488
5	2791	488
6	3319	488
7	4123	488
8	4967	488
9	4904	488

prune20.0ms (0.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	21	8	29

Error

2.9b

Counts

29 → 8

Alt Table

Status	Error	Program
	26.5b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) t)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) t)))))
✓	26.4b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))
	32.6b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (+.f64 z (sqrt.f64 t))) (-.f64 z (sqrt.f64 t))))
✓	20.1b	(fma.f64 4 (.f64 t y) (.f64 x x))
	42.9b	(-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 (pow.f64 z 6) (pow.f64 t 3)) (*.f64 4 y)) (fma.f64 t (fma.f64 z z t) (pow.f64 z 4))))
▶	21.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x))) (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x)))) (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x))))
	35.3b	(exp.f64 (log.f64 (fma.f64 4 (.f64 t y) (.f64 x x))))
✓	7.3b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))

Compiler

Compiled 600 to 305 computations (49.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (.f64 t y) (.f64 x x))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x))) (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x)))) (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x))))
✓	0.6b	(.f64 (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x))) (cbrt.f64 (fma.f64 4 (.f64 t y) (*.f64 x x))))
✓	2.9b	(cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x)))

series139.0ms (2.2%)

Counts

3 → 108

Calls

3 calls:

68.0ms

(*.f64 (cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x))) (cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x))))

58.0ms

(cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x)))

13.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x))) (cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x)))) (cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x))))

rewrite18.0ms (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 4 (*.f64 t y) (*.f64 x x))) (cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x)))) (cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x))))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x))) (cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x))))

1.0ms

(cbrt.f64 (fma.f64 4 (*.f64 t y) (*.f64 x x)))

simplify139.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

329×	`unswap-sqr_binary64`
298×	`associate-r_binary64`
234×	`associate-/r*_binary64`
223×	`associate-l_binary64`
219×	`times-frac_binary64`

Counts

201 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	362	6909
1	1077	6543
2	3926	6145
3	5062	6145

prune666.0ms (10.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	440	6	446
Fresh	1	3	4
Picked	1	0	1
Done	0	3	3
Total	442	12	454

Error

2.9b

Counts

454 → 12

Alt Table

Status	Error	Program
	40.9b	(.f64 (pow.f64 (.f64 (fma.f64 4 (.f64 t y) (.f64 x x)) (fma.f64 4 (.f64 t y) (.f64 x x))) 1/3) (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x))))
	32.6b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (+.f64 z (sqrt.f64 t))) (-.f64 z (sqrt.f64 t))))
	26.5b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) t)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) t)))))
✓	26.4b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))
	42.9b	(-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 (pow.f64 z 6) (pow.f64 t 3)) (*.f64 4 y)) (fma.f64 t (fma.f64 z z t) (pow.f64 z 4))))
	57.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x))) (+.f64 (.f64 1/12 (.f64 (pow.f64 (/.f64 4 (.f64 (pow.f64 y 2) (pow.f64 t 2))) 1/3) (pow.f64 x 2))) (pow.f64 (.f64 4 (.f64 y t)) 1/3))) (cbrt.f64 (fma.f64 4 (.f64 t y) (*.f64 x x))))
✓	7.3b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
	58.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x))) (cbrt.f64 (fma.f64 4 (.f64 t y) (.f64 x x)))) (+.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (.f64 4 y))) (log.f64 (/.f64 -1 t))))) (.f64 1/12 (/.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (.f64 4 y))) (log.f64 (/.f64 -1 t))))) (pow.f64 x 2)) (*.f64 y t)))))
	41.1b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 t 4)))) 6) 1/3) (cbrt.f64 (fma.f64 4 (.f64 t y) (*.f64 x x))))
✓	20.1b	(fma.f64 4 (.f64 t y) (.f64 x x))
	31.2b	(expm1.f64 (log1p.f64 (fma.f64 x x (.f64 y (.f64 t 4)))))
	35.5b	(.f64 (pow.f64 (fma.f64 4 (.f64 t y) (.f64 x x)) 2/3) (cbrt.f64 (fma.f64 4 (.f64 t y) (*.f64 x x))))

Compiler

Compiled 20627 to 11411 computations (44.7% saved)

regimes1.6s (26.2%)

Accuracy

Total 0.5b remaining (17.1%)

Threshold costs 0.5b (17.1%)

Counts

107 → 2

Compiler

Compiled 26378 to 17106 computations (35.2% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
16×	`*-commutative_binary64`
16×	`sub-neg_binary64`
15×	`distribute-rgt-neg-in_binary64`
14×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	54
1	41	54
2	77	54
3	107	54
4	148	54
5	165	54
6	167	54
7	162	54

end207.0ms (3.3%)

Compiler: Compiled 426 to 261 computations (38.7% saved)

Details

analyze910.0ms (14.5%)

sample1.6s (25.1%)

simplify62.0ms (1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series59.0ms (0.9%)

rewrite20.0ms (0.3%)

simplify97.0ms (1.5%)

prune133.0ms (2.1%)

localize11.0ms (0.2%)

series116.0ms (1.8%)

rewrite36.0ms (0.6%)

simplify124.0ms (2%)

prune163.0ms (2.6%)

localize5.0ms (0.1%)

series14.0ms (0.2%)

rewrite1.0ms (0%)

simplify84.0ms (1.3%)

prune20.0ms (0.3%)

localize10.0ms (0.2%)

series139.0ms (2.2%)

rewrite18.0ms (0.3%)

simplify139.0ms (2.2%)

prune666.0ms (10.6%)

regimes1.6s (26.2%)

bsearch4.0ms (0.1%)

simplify6.0ms (0.1%)

end207.0ms (3.3%)

Profiling