Details

analyze7.0ms (0.2%)

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)

sample791.0ms (26.7%)

Results

760.0ms	8251×	body	128	valid
1.0ms	3×	body	1024	valid
0.0ms	2×	body	512	valid
0.0ms	3×	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 (0.1%)

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)

simplify110.0ms (3.7%)

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

prune10.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	13	2	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Error

0.1b

Counts

16 → 3

Alt Table

Status	Error	Program
▶	15.9b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	20.6b	(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)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 166 to 136 computations (18.1% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 841/108 x 4/29))
	0.1b	(fma.f64 841/108 x 4/29)
✓	0.1b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))

series10.0ms (0.3%)

Counts

2 → 16

Calls

2 calls:

8.0ms	(sqrt.f64 (fma.f64 841/108 x 4/29))
2.0ms	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

7.0ms	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
1.0ms	(sqrt.f64 (fma.f64 841/108 x 4/29))

simplify100.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

454×	`fma-def_binary64`
417×	`times-frac_binary64`
363×	`associate-/l*_binary64`
271×	`distribute-lft-in_binary64`
271×	`distribute-rgt-in_binary64`

Counts

84 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	796
1	143	736
2	393	716
3	1299	662
4	4570	662
5	4715	662
6	4812	662
7	5097	662

prune122.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	136	7	143

Error

0.0b

Counts

143 → 7

Alt Table

Status	Error	Program
▶	16.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))
	20.6b	(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)))
	16.8b	(.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (.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)))))
	16.8b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))))
	22.4b	(.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29)))))
✓	0.1b	(fma.f64 841/108 x 4/29)
	17.3b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 5) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))

Compiler

Compiled 2442 to 2073 computations (15.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series19.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

8.0ms

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

6.0ms

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

5.0ms

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

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
56×	`cbrt-prod_binary64`
34×	`sqrt-prod_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`

Counts

3 → 110

Calls

3 calls:

6.0ms

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

5.0ms

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

1.0ms

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

simplify185.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-def_binary64`
486×	`fma-neg_binary64`
307×	`*-commutative_binary64`
196×	`cancel-sign-sub-inv_binary64`
180×	`times-frac_binary64`

Counts

146 → 215

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	235	4190
1	569	3840
2	1619	3119
3	4293	3048
4	4981	3048
5	4938	3048

prune485.0ms (16.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	367	2	369
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	367	9	376

Error

0.0b

Counts

376 → 9

Alt Table

Status	Error	Program
✓	16.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))
	20.6b	(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)))
	16.8b	(.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (.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)))))
	16.8b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))))
	22.4b	(.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29)))))
▶	16.6b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (exp.f64 (log.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))
	16.8b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (exp.f64 (log.f64 (fma.f64 841/108 x 4/29))))))
✓	0.1b	(fma.f64 841/108 x 4/29)
	17.3b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 5) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))

Compiler

Compiled 13339 to 11427 computations (14.3% saved)

localize17.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series11.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(exp.f64 (log.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))))
5.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (exp.f64 (log.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
32×	`cbrt-prod_binary64`
27×	`exp-sum_binary64`
27×	`log-prod_binary64`
16×	`sqrt-prod_binary64`

Counts

2 → 70

Calls

2 calls:

9.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (exp.f64 (log.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))))
2.0ms	(exp.f64 (log.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))))

simplify152.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-neg_binary64`
395×	`fma-def_binary64`
304×	`unswap-sqr_binary64`
290×	`associate-l_binary64`
285×	`associate-r_binary64`

Counts

94 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	190	2579
1	400	2409
2	1060	2084
3	3425	1811
4	4868	1795
5	4938	1795
6	5000	1795
7	4915	1795

prune437.0ms (14.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	359	0	359
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	359	9	368

Error

0.0b

Counts

368 → 9

Alt Table

Status	Error	Program
✓	16.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))
	20.6b	(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)))
	16.8b	(.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (.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)))))
	16.8b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))))
	22.4b	(.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29)))))
✓	16.6b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (exp.f64 (log.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))
	16.8b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (exp.f64 (log.f64 (fma.f64 841/108 x 4/29))))))
✓	0.1b	(fma.f64 841/108 x 4/29)
	17.3b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 5) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))

Compiler

Compiled 13952 to 12023 computations (13.8% saved)

regimes269.0ms (9.1%)

Accuracy

Total 0.0b remaining (32.5%)

Threshold costs 0.0b (32.5%)

Counts

76 → 1

Compiler

Compiled 4106 to 3518 computations (14.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end159.0ms (5.4%)

Compiler: Compiled 210 to 178 computations (15.2% saved)

Details

analyze7.0ms (0.2%)

sample791.0ms (26.7%)

simplify6.0ms (0.2%)

prune2.0ms (0.1%)

localize2.0ms (0.1%)

series2.0ms (0.1%)

rewrite1.0ms (0%)

simplify110.0ms (3.7%)

prune10.0ms (0.3%)

localize5.0ms (0.2%)

series10.0ms (0.3%)

rewrite11.0ms (0.4%)

simplify100.0ms (3.4%)

prune122.0ms (4.1%)

localize9.0ms (0.3%)

series19.0ms (0.6%)

rewrite23.0ms (0.8%)

simplify185.0ms (6.2%)

prune485.0ms (16.4%)

localize17.0ms (0.6%)

series11.0ms (0.4%)

rewrite18.0ms (0.6%)

simplify152.0ms (5.1%)

prune437.0ms (14.7%)

regimes269.0ms (9.1%)

simplify3.0ms (0.1%)

end159.0ms (5.4%)

Profiling