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)

sample806.0ms (24%)

Results

773.0ms	8246×	body	128	valid
2.0ms	6×	body	1024	valid
0.0ms	3×	body	256	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

prune4.0ms (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 (0.1%)

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)

simplify112.0ms (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

prune12.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	11	4	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	5	16

Error

0.0b

Counts

16 → 5

Alt Table

Status	Error	Program
	17.8b	(exp.f64 (log.f64 (fma.f64 841/108 x 4/29)))
✓	0.1b	(fma.f64 841/108 x 4/29)
	16.7b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
▶	1.9b	(.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)))
	20.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)))

Compiler

Compiled 216 to 178 computations (17.6% saved)

localize11.0ms (0.3%)

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))

series12.0ms (0.4%)

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)))

rewrite20.0ms (0.6%)

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))

simplify106.0ms (3.2%)

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

prune275.0ms (8.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	318	6	324
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	321	8	329

Error

0.0b

Counts

329 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)
	2.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
	17.8b	(exp.f64 (log.f64 (fma.f64 841/108 x 4/29)))
	45.1b	(.f64 (fma.f64 288/24389 (/.f64 (cbrt.f64 (.f64 707281/11664 (pow.f64 (/.f64 -1 x) -2))) x) (cbrt.f64 (*.f64 707281/11664 (pow.f64 (/.f64 -1 x) -2)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	31.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (fma.f64 144/24389 (/.f64 (cbrt.f64 (/.f64 -841/108 (/.f64 -1 x))) x) (cbrt.f64 (/.f64 -841/108 (/.f64 -1 x)))))
▶	1.0b	(.f64 (.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)))
	2.0b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (.f64 (cbrt.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)))

Compiler

Compiled 8321 to 7020 computations (15.6% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))
	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))
✓	0.8b	(cbrt.f64 (fma.f64 x 841/108 4/29))
✓	1.0b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5)

series33.0ms (1%)

Counts

3 → 36

Calls

3 calls:

22.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5)
6.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))
5.0ms	(cbrt.f64 (fma.f64 x 841/108 4/29))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`

Counts

3 → 55

Calls

3 calls:

2.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5)
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))
1.0ms	(cbrt.f64 (fma.f64 x 841/108 4/29))

simplify94.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
429×	`associate-r_binary64`
424×	`associate-l_binary64`
390×	`fma-neg_binary64`
216×	`times-frac_binary64`

Counts

91 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	225	2442
1	551	2323
2	1470	2033
3	4852	2033
4	5082	2033

prune255.0ms (7.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	238	8	246

Error

0.0b

Counts

246 → 8

Alt Table

Status	Error	Program
	45.1b	(.f64 (fma.f64 288/24389 (/.f64 (cbrt.f64 (.f64 707281/11664 (pow.f64 (/.f64 -1 x) -2))) x) (cbrt.f64 (*.f64 707281/11664 (pow.f64 (/.f64 -1 x) -2)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	2.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6)) (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)))
✓	0.1b	(fma.f64 841/108 x 4/29)
	2.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
	17.8b	(exp.f64 (log.f64 (fma.f64 841/108 x 4/29)))
	31.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (fma.f64 144/24389 (/.f64 (cbrt.f64 (/.f64 -841/108 (/.f64 -1 x))) x) (cbrt.f64 (/.f64 -841/108 (/.f64 -1 x)))))
	2.0b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
▶	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (.f64 (cbrt.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)))

Compiler

Compiled 8322 to 7185 computations (13.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

8.0ms

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

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`cbrt-prod_binary64`
32×	`add-sqr-sqrt_binary64`
23×	`pow1_binary64`
22×	`pow1/3_binary64`
16×	`add-exp-log_binary64`

Counts

2 → 85

Calls

2 calls:

10.0ms

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

simplify112.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

492×	`times-frac_binary64`
419×	`fma-def_binary64`
307×	`fma-neg_binary64`
291×	`cancel-sign-sub-inv_binary64`
245×	`*-commutative_binary64`

Counts

109 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	3197
1	456	2854
2	1262	2322
3	3243	2148
4	4937	2148

prune641.0ms (19.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	548	1	549
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	548	9	557

Error

0.0b

Counts

557 → 9

Alt Table

Status	Error	Program
	45.1b	(.f64 (fma.f64 288/24389 (/.f64 (cbrt.f64 (.f64 707281/11664 (pow.f64 (/.f64 -1 x) -2))) x) (cbrt.f64 (*.f64 707281/11664 (pow.f64 (/.f64 -1 x) -2)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	2.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6)) (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)))
✓	0.1b	(fma.f64 841/108 x 4/29)
	2.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
	17.8b	(exp.f64 (log.f64 (fma.f64 841/108 x 4/29)))
	31.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (fma.f64 144/24389 (/.f64 (cbrt.f64 (/.f64 -841/108 (/.f64 -1 x))) x) (cbrt.f64 (/.f64 -841/108 (/.f64 -1 x)))))
	2.1b	(.f64 (.f64 (.f64 (.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))))) (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)))))) (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)))))) (.f64 (cbrt.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)))
	2.0b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
✓	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (.f64 (cbrt.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)))

Compiler

Compiled 23430 to 19955 computations (14.8% saved)

regimes484.0ms (14.4%)

Accuracy

Total 0.0b remaining (40.1%)

Threshold costs 0.0b (40.1%)

Counts

126 → 1

Compiler

Compiled 8414 to 7187 computations (14.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end300.0ms (8.9%)

Compiler: Compiled 266 to 227 computations (14.7% saved)

Details

analyze4.0ms (0.1%)

sample806.0ms (24%)

simplify6.0ms (0.2%)

prune4.0ms (0.1%)

localize2.0ms (0.1%)

series2.0ms (0.1%)

rewrite1.0ms (0%)

simplify112.0ms (3.3%)

prune12.0ms (0.3%)

localize11.0ms (0.3%)

series12.0ms (0.4%)

rewrite20.0ms (0.6%)

simplify106.0ms (3.2%)

prune275.0ms (8.2%)

localize15.0ms (0.4%)

series33.0ms (1%)

rewrite6.0ms (0.2%)

simplify94.0ms (2.8%)

prune255.0ms (7.6%)

localize9.0ms (0.3%)

series13.0ms (0.4%)

rewrite23.0ms (0.7%)

simplify112.0ms (3.3%)

prune641.0ms (19.1%)

regimes484.0ms (14.4%)

simplify2.0ms (0.1%)

end300.0ms (8.9%)

Profiling