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)

sample954.0ms (25.5%)

Results

924.0ms	8253×	body	128	valid
1.0ms	2×	body	1024	valid
0.0ms	3×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 32 to 29 computations (9.4% saved)

simplify8.0ms (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)

simplify108.0ms (2.9%)

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

prune15.0ms (0.4%)

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
	15.7b	(*.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)))
	22.6b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))
	17.0b	(expm1.f64 (log1p.f64 (fma.f64 841/108 x 4/29)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 200 to 166 computations (17% saved)

localize6.0ms (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)))
✓	0.8b	(*.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 (0.3%)

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)))

rewrite20.0ms (0.5%)

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:

9.0ms

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

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)))

1.0ms

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

simplify136.0ms (3.6%)

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

prune258.0ms (6.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	318	6	324
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	320	9	329

Error

0.0b

Counts

329 → 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))) (.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 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	17.0b	(expm1.f64 (log1p.f64 (fma.f64 841/108 x 4/29)))
	17.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (expm1.f64 (log1p.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	48.1b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 707281/11664)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	27.6b	(pow.f64 (.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/3)
	1.9b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)
	22.6b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))
	2.3b	(.f64 (.f64 (.f64 (cbrt.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 (.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)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 8271 to 6974 computations (15.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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	(*.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))

series14.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(*.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	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))

rewrite13.0ms (0.3%)

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:

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

simplify115.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

531×	`fma-neg_binary64`
406×	`fma-def_binary64`
363×	`associate-l_binary64`
314×	`associate-r_binary64`
295×	`unswap-sqr_binary64`

Counts

96 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	2844
1	406	2644
2	1083	2258
3	3497	2075
4	4959	2075
5	4903	2075

prune703.0ms (18.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	574	2	576
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	575	10	585

Error

0.0b

Counts

585 → 10

Alt Table

Status	Error	Program
	48.1b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 707281/11664)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	16.5b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))))) (.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 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	22.6b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))
▶	1.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 5) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (cbrt.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))) (.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 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	17.0b	(expm1.f64 (log1p.f64 (fma.f64 841/108 x 4/29)))
	17.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (expm1.f64 (log1p.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	27.6b	(pow.f64 (.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/3)
	2.3b	(.f64 (.f64 (.f64 (cbrt.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 (.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)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 25018 to 21319 computations (14.8% saved)

localize18.0ms (0.5%)

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))
✓	1.0b	(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 5)

series31.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

20.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 5)
5.0ms	(cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))))
5.0ms	(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)))) 5)
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))

simplify106.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

573×	`fma-def_binary64`
437×	`associate-l_binary64`
436×	`associate-r_binary64`
390×	`fma-neg_binary64`
216×	`times-frac_binary64`

Counts

97 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	2715
1	547	2602
2	1482	2306
3	4880	2306
4	5109	2306

prune474.0ms (12.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	327	1	328
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	328	10	338

Error

0.0b

Counts

338 → 10

Alt Table

Status	Error	Program
	48.1b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 707281/11664)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	16.5b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))))) (.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 (cbrt.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))) (.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 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	17.0b	(expm1.f64 (log1p.f64 (fma.f64 841/108 x 4/29)))
	16.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29)))))) 5) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	17.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (expm1.f64 (log1p.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	27.6b	(pow.f64 (.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/3)
	22.6b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))
	2.3b	(.f64 (.f64 (.f64 (cbrt.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 (.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)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 16042 to 13865 computations (13.6% saved)

regimes473.0ms (12.7%)

Accuracy

Total 0.0b remaining (38.5%)

Threshold costs 0.0b (38.5%)

Counts

110 → 1

Compiler

Compiled 9572 to 8246 computations (13.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end244.0ms (6.5%)

Compiler: Compiled 252 to 213 computations (15.5% saved)

Details

analyze4.0ms (0.1%)

sample954.0ms (25.5%)

simplify8.0ms (0.2%)

prune2.0ms (0.1%)

localize2.0ms (0.1%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify108.0ms (2.9%)

prune15.0ms (0.4%)

localize6.0ms (0.2%)

series12.0ms (0.3%)

rewrite20.0ms (0.5%)

simplify136.0ms (3.6%)

prune258.0ms (6.9%)

localize9.0ms (0.2%)

series14.0ms (0.4%)

rewrite13.0ms (0.3%)

simplify115.0ms (3.1%)

prune703.0ms (18.8%)

localize18.0ms (0.5%)

series31.0ms (0.8%)

rewrite7.0ms (0.2%)

simplify106.0ms (2.8%)

prune474.0ms (12.7%)

regimes473.0ms (12.7%)

simplify2.0ms (0%)

end244.0ms (6.5%)

Profiling