Details

analyze42.0ms (1.4%)

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)

sample28.0ms (0.9%)

Algorithm

1×

intervals

Results

16.0ms	255×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 22 to 20 computations (9.1% saved)

simplify20.0ms (0.6%)

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

prune5.0ms (0.2%)

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)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64`
5×	`fma-udef_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

1 → 33

Calls

1 calls:

18.0ms

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

series19.0ms (0.6%)

Counts

1 → 12

Calls

1 calls:

19.0ms

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

simplify105.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

561×	`fma-def_binary64`
482×	`fma-neg_binary64`
462×	`unswap-sqr_binary64`
417×	`associate-+l+_binary64`
342×	`associate-+r+_binary64`

Counts

45 → 60

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	275
1	88	255
2	200	254
3	410	253
4	783	250
5	1777	250
6	2966	250
7	4605	250
8	4906	250

prune46.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	55	5	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	6	61

Error

0.0b

Counts

61 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)
	16.9b	(pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)
	16.2b	(/.f64 (fma.f64 x (*.f64 x 707281/11664) -16/841) (fma.f64 841/108 x -4/29))
	20.7b	(/.f64 (fma.f64 594823321/1259712 (pow.f64 x 3) 64/24389) (fma.f64 x (fma.f64 x 707281/11664 -29/27) 16/841))
	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)))
▶	1.8b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)

Compiler

Compiled 423 to 349 computations (17.5% saved)

localize16.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 841/108 x 4/29)
✓	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))
✓	0.9b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)

rewrite53.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cube-cbrt_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`pow1/3_binary64`
6×	`log1p-expm1-u_binary64`
6×	`expm1-log1p-u_binary64`

Counts

2 → 75

Calls

2 calls:

29.0ms	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)
18.0ms	(cbrt.f64 (fma.f64 841/108 x 4/29))

series404.0ms (13.1%)

Counts

2 → 24

Calls

2 calls:

389.0ms	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)
15.0ms	(cbrt.f64 (fma.f64 841/108 x 4/29))

simplify114.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

722×	`times-frac_binary64`
478×	`associate-l_binary64`
438×	`associate-r_binary64`
254×	`fma-neg_binary64`
219×	`fma-def_binary64`

Counts

99 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1350
1	289	1247
2	793	1137
3	3380	887
4	5148	887

prune89.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	3	1	4
Picked	1	0	1
Done	1	0	1
Total	227	4	231

Error

0.0b

Counts

231 → 4

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)))
	33.7b	(/.f64 -841/108 (/.f64 -1 x))
	0.2b	(fma.f64 432/24389 (/.f64 (.f64 x 841/108) x) (.f64 x 841/108))
▶	0.1b	(+.f64 (.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x)) (pow.f64 64/24389 1/3))

Compiler

Compiled 2036 to 1771 computations (13% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x)) (pow.f64 64/24389 1/3))
✓	0.1b	(*.f64 (pow.f64 64/24389 1/3) x)
✓	0.3b	(.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x))

rewrite52.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`add-exp-log_binary64`
12×	`add-cbrt-cube_binary64`

Counts

3 → 112

Calls

3 calls:

17.0ms	(+.f64 (.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x)) (pow.f64 64/24389 1/3))
15.0ms	(.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x))
15.0ms	(*.f64 (pow.f64 64/24389 1/3) x)

series717.0ms (23.3%)

Counts

3 → 9

Calls

3 calls:

338.0ms	(.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x))
247.0ms	(*.f64 (pow.f64 64/24389 1/3) x)
132.0ms	(+.f64 (.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x)) (pow.f64 64/24389 1/3))

simplify128.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-neg_binary64`
522×	`times-frac_binary64`
327×	`fma-def_binary64`
292×	`*-commutative_binary64`
241×	`div-sub_binary64`

Counts

121 → 198

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	120	1330
1	268	1222
2	1036	1185
3	3467	1178
4	4829	1176
5	5000	1176
6	4755	1176

prune118.0ms (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	198	4	202

Error

0.0b

Counts

202 → 4

Alt Table

Status	Error	Program
	0.3b	(+.f64 (.f64 (.f64 (cbrt.f64 24389/432) (cbrt.f64 24389/432)) (.f64 (.f64 (cbrt.f64 64/24389) x) (cbrt.f64 24389/432))) (pow.f64 64/24389 1/3))
▶	0.2b	(fma.f64 432/24389 (/.f64 (.f64 x 841/108) x) (.f64 x 841/108))
✓	0.1b	(+.f64 (.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x)) (pow.f64 64/24389 1/3))
	1.8b	(pow.f64 (cbrt.f64 (+.f64 (.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x)) (pow.f64 64/24389 1/3))) 3)

Compiler

Compiled 2682 to 2430 computations (9.4% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 432/24389 (/.f64 (.f64 x 841/108) x) (.f64 x 841/108))
	0.2b	(*.f64 x 841/108)
✓	0.2b	(*.f64 x 841/108)
✓	0.3b	(/.f64 (*.f64 x 841/108) x)

rewrite38.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
16×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`

Counts

3 → 115

Calls

3 calls:

13.0ms	(/.f64 (*.f64 x 841/108) x)
12.0ms	(*.f64 x 841/108)
9.0ms	(fma.f64 432/24389 (/.f64 (.f64 x 841/108) x) (.f64 x 841/108))

series13.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(fma.f64 432/24389 (/.f64 (.f64 x 841/108) x) (.f64 x 841/108))
5.0ms	(*.f64 x 841/108)
0.0ms	(/.f64 (*.f64 x 841/108) x)

simplify95.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

578×	`associate-l_binary64`
487×	`associate-/l*_binary64`
446×	`fma-neg_binary64`
432×	`associate-r_binary64`
274×	`associate-/r*_binary64`

Counts

151 → 224

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	1165
1	242	650
2	903	630
3	4027	630
4	4986	628
5	4715	628

prune130.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	292	1	293
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	294	3	297

Error

Counts

297 → 3

Alt Table

Status	Error	Program
	0.3b	(fma.f64 432/24389 (/.f64 (.f64 x 841/108) x) (.f64 (.f64 x (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108))) (cbrt.f64 841/108)))
	0.3b	(+.f64 (.f64 (.f64 (cbrt.f64 24389/432) (cbrt.f64 24389/432)) (.f64 (.f64 (cbrt.f64 64/24389) x) (cbrt.f64 24389/432))) (pow.f64 64/24389 1/3))
✓	0.2b	(fma.f64 432/24389 (/.f64 (.f64 x 841/108) x) (.f64 x 841/108))

Compiler

Compiled 2708 to 1992 computations (26.4% saved)

regimes316.0ms (10.3%)

Accuracy

Total 0.1b remaining (92.3%)

Threshold costs 0.1b (92.3%)

Compiler

Compiled 3598 to 3118 computations (13.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

sample494.0ms (16%)

Algorithm

1×

intervals

Results

283.0ms	7997×	body	128	valid
0.0ms	2×	body	512	valid
0.0ms	3×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 64 to 55 computations (14.1% saved)

Details

analyze42.0ms (1.4%)

sample28.0ms (0.9%)

simplify20.0ms (0.6%)

prune5.0ms (0.2%)

localize5.0ms (0.2%)

rewrite20.0ms (0.7%)

series19.0ms (0.6%)

simplify105.0ms (3.4%)

prune46.0ms (1.5%)

localize16.0ms (0.5%)

rewrite53.0ms (1.7%)

series404.0ms (13.1%)

simplify114.0ms (3.7%)

prune89.0ms (2.9%)

localize7.0ms (0.2%)

rewrite52.0ms (1.7%)

series717.0ms (23.3%)

simplify128.0ms (4.1%)

prune118.0ms (3.8%)

localize5.0ms (0.2%)

rewrite38.0ms (1.2%)

series13.0ms (0.4%)

simplify95.0ms (3.1%)

prune130.0ms (4.2%)

regimes316.0ms (10.3%)

simplify5.0ms (0.2%)

end0.0ms (0%)

sample494.0ms (16%)

Profiling