Details

analyze76.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
50%	50%	0.1%	6
62.4%	31.2%	6.3%	7
71.8%	21.9%	6.3%	8
76.5%	14%	9.5%	9
80.4%	10.1%	9.5%	10
82.3%	6.6%	11%	11
84.1%	4.9%	11%	12
85%	3.2%	11.8%	13
85.8%	2.4%	11.8%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample785.0ms (13.7%)

Results

749.0ms	8256×	body	128	valid
6.0ms	66×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
13×	`distribute-lft-in_binary64`
13×	`distribute-rgt-in_binary64`
10×	`*-commutative_binary64`
9×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	10
1	18	10
2	32	8
3	56	8
4	68	8
5	74	8
6	66	8

prune4.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
▶	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 55 to 43 computations (21.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 x (/.f64 16 116)) 3)
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

series7.0ms (0.1%)

Counts

2 → 36

Calls

2 calls:

5.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
2.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`associate-l_binary64`

Counts

2 → 47

Calls

2 calls:

8.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)
7.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

simplify102.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
495×	`associate-r_binary64`
206×	`sqr-pow_binary64`
195×	`distribute-rgt-in_binary64`
194×	`distribute-lft-in_binary64`

Counts

83 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	921
1	206	672
2	611	666
3	1677	666
4	2385	666
5	3622	666
6	4778	666
7	4997	666
8	4869	666

prune71.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	8	85
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	78	9	87

Error

Counts

87 → 9

Alt Table

Status	Error	Program
	30.9b	(.f64 (.f64 (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 16) (sqrt.f64 116))) (fma.f64 3 (sqrt.f64 x) (/.f64 -12 (sqrt.f64 116)))) y)
	34.3b	(.f64 (.f64 (fma.f64 3 x -12/29) (sqrt.f64 y)) (sqrt.f64 y))
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	18.3b	(/.f64 (.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 (/.f64 16 116) 3)) 3) y) (+.f64 (.f64 x x) (+.f64 (.f64 (/.f64 16 116) (/.f64 16 116)) (*.f64 x (/.f64 16 116)))))
	17.0b	(.f64 (/.f64 (fma.f64 3 (pow.f64 x 3) -192/24389) (+.f64 (.f64 x x) (+.f64 (.f64 (/.f64 16 116) (/.f64 16 116)) (.f64 x (/.f64 16 116))))) y)
	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	13.4b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
▶	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
	29.6b	(.f64 (sqrt.f64 (.f64 y (fma.f64 3 x -12/29))) (sqrt.f64 (*.f64 y (fma.f64 3 x -12/29))))

Compiler

Compiled 1505 to 1177 computations (21.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 y (-.f64 x 4/29))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

series10.0ms (0.2%)

Counts

2 → 28

Calls

2 calls:

6.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
4.0ms	(*.f64 y (-.f64 x 4/29))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`

Counts

2 → 124

Calls

2 calls:

8.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
5.0ms	(*.f64 y (-.f64 x 4/29))

simplify102.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
474×	`*-commutative_binary64`
412×	`unsub-neg_binary64`
391×	`neg-mul-1_binary64`
389×	`neg-sub0_binary64`

Counts

152 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	1710
1	293	1349
2	721	1349
3	1730	1347
4	3194	1347
5	4989	1347
6	4900	1347

prune148.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	167	8	175

Error

Counts

175 → 8

Alt Table

Status	Error	Program
	30.9b	(.f64 (.f64 (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 16) (sqrt.f64 116))) (fma.f64 3 (sqrt.f64 x) (/.f64 -12 (sqrt.f64 116)))) y)
	34.3b	(.f64 (.f64 (fma.f64 3 x -12/29) (sqrt.f64 y)) (sqrt.f64 y))
▶	0.5b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y (-.f64 x 4/29))))
	18.1b	(/.f64 (.f64 3 (.f64 y (-.f64 (pow.f64 x 3) (pow.f64 4/29 3)))) (+.f64 (.f64 x x) (+.f64 (.f64 4/29 4/29) (*.f64 x 4/29))))
	18.1b	(.f64 3 (/.f64 (.f64 y (-.f64 (pow.f64 x 3) 64/24389)) (+.f64 (.f64 x x) (+.f64 (.f64 4/29 4/29) (*.f64 x 4/29)))))
	13.4b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 3348 to 2589 computations (22.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 y (-.f64 x 4/29))
✓	0.3b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y (-.f64 x 4/29))))
✓	0.4b	(.f64 (cbrt.f64 3) (.f64 y (-.f64 x 4/29)))

series42.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y (-.f64 x 4/29))))
14.0ms	(.f64 (cbrt.f64 3) (.f64 y (-.f64 x 4/29)))

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

208×	`distribute-lft-in_binary64`
208×	`distribute-rgt-in_binary64`
108×	`prod-diff_binary64`
88×	`*-un-lft-identity_binary64`
88×	`add-sqr-sqrt_binary64`

Counts

2 → 213

Calls

2 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y (-.f64 x 4/29))))
10.0ms	(.f64 (cbrt.f64 3) (.f64 y (-.f64 x 4/29)))

simplify138.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
698×	`*-commutative_binary64`
673×	`distribute-rgt-neg-out_binary64`
425×	`associate-l_binary64`
422×	`associate-r_binary64`

Counts

261 → 251

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	367	4314
1	431	2873
2	1092	2873
3	3094	2871
4	5802	2871

prune307.0ms (5.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	322	2	324
Fresh	3	2	5
Picked	1	0	1
Done	0	2	2
Total	326	6	332

Error

Counts

332 → 6

Alt Table

Status	Error	Program
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
▶	0.4b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (sqrt.f64 3)) (.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y (-.f64 x 4/29)))))
	18.1b	(.f64 3 (/.f64 (.f64 y (-.f64 (pow.f64 x 3) 64/24389)) (+.f64 (.f64 x x) (+.f64 (.f64 4/29 4/29) (*.f64 x 4/29)))))
	13.4b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
	0.5b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (cbrt.f64 (cbrt.f64 3)) (.f64 y (-.f64 x 4/29)))))
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 9758 to 8295 computations (15% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 y (-.f64 x 4/29))
✓	0.2b	(.f64 (cbrt.f64 (sqrt.f64 3)) (.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y (-.f64 x 4/29))))
✓	0.3b	(.f64 (cbrt.f64 (sqrt.f64 3)) (.f64 y (-.f64 x 4/29)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (sqrt.f64 3)) (.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y (-.f64 x 4/29)))))

series949.0ms (16.5%)

Counts

3 → 72

Calls

3 calls:

393.0ms

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y (-.f64 x 4/29)))))

331.0ms

(*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y (-.f64 x 4/29))))

224.0ms

(*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y (-.f64 x 4/29)))

rewrite132.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

624×	`distribute-lft-in_binary64`
624×	`distribute-rgt-in_binary64`
252×	`prod-diff_binary64`
205×	`*-un-lft-identity_binary64`
205×	`add-sqr-sqrt_binary64`

Counts

3 → 461

Calls

3 calls:

23.0ms

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y (-.f64 x 4/29)))))

17.0ms

(*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y (-.f64 x 4/29))))

8.0ms

(*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y (-.f64 x 4/29)))

simplify356.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

869×	`associate-r_binary64`
835×	`associate-l_binary64`
638×	`*-commutative_binary64`
482×	`distribute-rgt-in_binary64`
450×	`distribute-lft-in_binary64`

Counts

533 → 529

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	679	22702
1	623	13466
2	1953	10844
3	4928	10844

prune1.1s (18.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	601	1	602
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	602	6	608

Error

Counts

608 → 6

Alt Table

Status	Error	Program
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
✓	0.4b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (sqrt.f64 3)) (.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y (-.f64 x 4/29)))))
	0.4b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (sqrt.f64 3)) (.f64 (*.f64 (cbrt.f64 (sqrt.f64 3)) y) (-.f64 x 4/29))))
	13.4b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
	0.5b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (cbrt.f64 (cbrt.f64 3)) (.f64 y (-.f64 x 4/29)))))
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 23722 to 20962 computations (11.6% saved)

regimes1.2s (21.3%)

Accuracy

Total 0.2b remaining (89%)

Threshold costs 0.2b (89%)

Counts

199 → 1

Compiler

Compiled 18028 to 15262 computations (15.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	13	13

end95.0ms (1.7%)

Compiler: Compiled 124 to 104 computations (16.1% saved)

Details

analyze76.0ms (1.3%)

sample785.0ms (13.7%)

simplify7.0ms (0.1%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series7.0ms (0.1%)

rewrite17.0ms (0.3%)

simplify102.0ms (1.8%)

prune71.0ms (1.2%)

localize4.0ms (0.1%)

series10.0ms (0.2%)

rewrite23.0ms (0.4%)

simplify102.0ms (1.8%)

prune148.0ms (2.6%)

localize9.0ms (0.2%)

series42.0ms (0.7%)

rewrite50.0ms (0.9%)

simplify138.0ms (2.4%)

prune307.0ms (5.3%)

localize11.0ms (0.2%)

series949.0ms (16.5%)

rewrite132.0ms (2.3%)

simplify356.0ms (6.2%)

prune1.1s (18.6%)

regimes1.2s (21.3%)

simplify2.0ms (0%)

end95.0ms (1.7%)

Profiling