Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.8%	0.1%	0.1%	12
99.8%	0%	0.1%	13
99.8%	0%	0.2%	14

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample752.0ms (22.4%)

Results

717.0ms	8255×	body	128	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 29 computations (9.4% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	16	5
3	14	5

prune2.0ms (0.1%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(fma.f64 841/108 x 4/29)

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 841/108 x 4/29)

simplify110.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

639×	`associate-*r/_binary64`
493×	`distribute-rgt-in_binary64`
446×	`distribute-lft-out_binary64`
406×	`distribute-rgt-out_binary64`
402×	`associate-l_binary64`

Counts

22 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	142
1	19	131
2	42	131
3	104	131
4	284	131
5	900	131
6	1555	131
7	2510	131
8	2614	131
9	3104	131
10	4503	131
11	4867	131
12	4989	131
13	4799	131

prune11.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Error

0.0b

Counts

16 → 4

Alt Table

Status	Error	Program
	18.9b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
▶	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	24.0b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 186 to 154 computations (17.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 841/108 x 4/29)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.7b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))

series11.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

5.0ms

(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))

5.0ms

(cbrt.f64 (fma.f64 841/108 x 4/29))

2.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))

rewrite15.0ms (0.4%)

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 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))

1.0ms

(cbrt.f64 (fma.f64 841/108 x 4/29))

simplify115.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

492×	`times-frac_binary64`
423×	`fma-def_binary64`
413×	`fma-neg_binary64`
239×	`unswap-sqr_binary64`
210×	`*-commutative_binary64`

Counts

129 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2495
1	418	2285
2	1171	1923
3	3158	1699
4	4947	1699
5	4970	1699

prune243.0ms (7.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	320	4	324
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	322	6	328

Error

0.0b

Counts

328 → 6

Alt Table

Status	Error	Program
✓	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	46.7b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 707281/11664)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
▶	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	1.8b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 4)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	1.9b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 8) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 8167 to 6887 computations (15.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
✓	0.3b	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.3b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))

series18.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))

5.0ms

(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))

4.0ms

(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`cbrt-prod_binary64`
39×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
17×	`pow1_binary64`

Counts

3 → 100

Calls

3 calls:

6.0ms

(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))

6.0ms

(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))

1.0ms

(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))

simplify124.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

615×	`fma-def_binary64`
480×	`fma-neg_binary64`
331×	`*-commutative_binary64`
204×	`cancel-sign-sub-inv_binary64`
180×	`times-frac_binary64`

Counts

136 → 221

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	4128
1	598	3780
2	1679	3093
3	4440	2978
4	4974	2978

prune646.0ms (19.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	551	3	554
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	551	9	560

Error

0.0b

Counts

560 → 9

Alt Table

Status	Error	Program
✓	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	46.7b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 707281/11664)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	19.7b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 2) (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	1.8b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 4)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	20.1b	(.f64 (.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	1.9b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 8) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
▶	1.3b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 4))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 23990 to 20483 computations (14.6% saved)

localize24.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))))
	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))
✓	0.8b	(cbrt.f64 (fma.f64 x 841/108 4/29))
✓	0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 4)

series20.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

11.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 4)
4.0ms	(cbrt.f64 (fma.f64 x 841/108 4/29))
4.0ms	(cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`unpow-prod-down_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 61

Calls

3 calls:

3.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 4)
1.0ms	(cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))))
1.0ms	(cbrt.f64 (fma.f64 x 841/108 4/29))

simplify100.0ms (3%)

Algorithm

1×	egg-herbie

Rules

558×	`fma-def_binary64`
432×	`associate-l_binary64`
429×	`associate-r_binary64`
384×	`fma-neg_binary64`
216×	`times-frac_binary64`

Counts

97 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	2691
1	537	2560
2	1455	2273
3	4837	2273
4	5064	2273

prune645.0ms (19.2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	378	0	378
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	378	9	387

Error

0.0b

Counts

387 → 9

Alt Table

Status	Error	Program
✓	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	46.7b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 707281/11664)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	19.7b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 2) (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	1.8b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 4)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	20.1b	(.f64 (.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	1.9b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 8) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
✓	1.3b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 4))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 21018 to 18147 computations (13.7% saved)

regimes281.0ms (8.4%)

Accuracy

Total 0.0b remaining (40.3%)

Threshold costs 0.0b (40.3%)

Counts

66 → 1

Compiler

Compiled 4841 to 4154 computations (14.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end189.0ms (5.6%)

Compiler: Compiled 227 to 193 computations (15% saved)

Details

analyze4.0ms (0.1%)

sample752.0ms (22.4%)

simplify6.0ms (0.2%)

prune2.0ms (0.1%)

localize2.0ms (0.1%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify110.0ms (3.3%)

prune11.0ms (0.3%)

localize8.0ms (0.2%)

series11.0ms (0.3%)

rewrite15.0ms (0.4%)

simplify115.0ms (3.4%)

prune243.0ms (7.2%)

localize8.0ms (0.2%)

series18.0ms (0.5%)

rewrite19.0ms (0.6%)

simplify124.0ms (3.7%)

prune646.0ms (19.2%)

localize24.0ms (0.7%)

series20.0ms (0.6%)

rewrite7.0ms (0.2%)

simplify100.0ms (3%)

prune645.0ms (19.2%)

regimes281.0ms (8.4%)

simplify2.0ms (0.1%)

end189.0ms (5.6%)

Profiling