Details

analyze4.0ms (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
50%	25%	25%	4
62.5%	12.5%	25%	5
62.5%	6.2%	31.3%	6
65.6%	3.1%	31.3%	7
65.6%	1.6%	32.8%	8
66.4%	0.8%	32.8%	9
66.4%	0.4%	33.2%	10
66.6%	0.2%	33.2%	11
66.6%	0.1%	33.3%	12
66.6%	0%	33.3%	13
66.6%	0%	33.3%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample755.0ms (37.9%)

Results

690.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify39.0ms (2%)

Algorithm

1×	egg-herbie

Rules

986×	`fma-neg_binary64`
313×	`distribute-rgt-neg-in_binary64`
301×	`associate-l_binary64`
241×	`fma-def_binary64`
233×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	21	11
2	55	11
3	135	11
4	228	11
5	392	11
6	762	11
7	1595	11
8	2514	11
9	3707	11
10	4623	11

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))

Status

Error

Program

▶

0.2b

(*.f64 x (fma.f64 x (*.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))

0.2b

(-.f64 (*.f64 238732414637843/250000000000000 x) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))

Compiler

Compiled 62 to 41 computations (33.9% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (*.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000)
✓	0.1b	(*.f64 x -6450306886639899/50000000000000000)
✓	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms

(*.f64 x (fma.f64 x (*.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))

2.0ms

(fma.f64 x (*.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000)

1.0ms

(*.f64 x -6450306886639899/50000000000000000)

rewrite49.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

597×	`log1p-expm1-u_binary64`
597×	`expm1-log1p-u_binary64`
308×	`log-prod_binary64`
123×	`pow1/3_binary64`
123×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
1	142	23
2	1604	23

Stop Event

1×	node limit

Counts

3 → 66

Calls

3 calls:

48.0ms

(fma.f64 x (*.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000)

48.0ms

(*.f64 x -6450306886639899/50000000000000000)

48.0ms

(*.f64 x (fma.f64 x (*.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))

simplify43.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
419×	`fma-neg_binary64`
402×	`distribute-rgt-neg-in_binary64`
375×	`distribute-lft-neg-in_binary64`
243×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	288
1	43	270
2	96	252
3	279	252
4	900	252
5	1768	252
6	2948	252
7	4338	252

Stop Event

1×	node limit

Counts

102 → 78

prune61.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Error

0.0b

Counts

80 → 8

Alt Table

Status	Error	Program
	0.2b	(.f64 x (fma.f64 -6450306886639899/50000000000000000 (.f64 x x) 238732414637843/250000000000000))
✓	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	27.4b	(pow.f64 (sqrt.f64 (.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))) 2)
	41.8b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000) 3)))
	16.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))))
	1.4b	(pow.f64 (cbrt.f64 (.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))) 3)
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))

Compiler

Compiled 1109 to 795 computations (28.3% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
✓	0.1b	(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))
✓	0.1b	(*.f64 238732414637843/250000000000000 x)

series7.0ms (0.4%)

Counts

3 → 3

Calls

3 calls:

3.0ms

(-.f64 (*.f64 238732414637843/250000000000000 x) (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))

3.0ms

(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))

1.0ms

(*.f64 238732414637843/250000000000000 x)

rewrite62.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`log-prod_binary64`
370×	`fma-def_binary64`
242×	`pow2_binary64`
192×	`egg-rr`
171×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	209	22
2	2539	22

Stop Event

1×	node limit

Counts

3 → 192

Calls

3 calls:

57.0ms

(-.f64 (*.f64 238732414637843/250000000000000 x) (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))

57.0ms

(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))

57.0ms

(*.f64 238732414637843/250000000000000 x)

simplify58.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

733×	`sqr-pow_binary64`
449×	`associate-l_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
256×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	18	18
2	35	18
3	60	18
4	118	18
5	328	18
6	1190	18
7	1877	18
8	1964	18
9	2097	18
10	2255	18
11	2489	18
12	2811	18
13	3232	18
14	3732	18
15	4325	18

Stop Event

1×	node limit

Counts

195 → 194

prune189.0ms (9.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	192	2	194
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	193	9	202

Error

Counts

202 → 9

Alt Table

Status	Error	Program
▶	0.2b	(.f64 x (fma.f64 -6450306886639899/50000000000000000 (.f64 x x) 238732414637843/250000000000000))
✓	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	27.4b	(pow.f64 (sqrt.f64 (.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))) 2)
	41.8b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000) 3)))
	16.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))))
	1.4b	(pow.f64 (cbrt.f64 (.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))) 3)
	29.8b	(-.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 13606116089006033875034270860295875508316107/15625000000000000000000000000000000000000000)) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	28.7b	(-.f64 (.f64 238732414637843/250000000000000 x) (pow.f64 (.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3/2)) 2))

Compiler

Compiled 4210 to 3340 computations (20.7% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 -6450306886639899/50000000000000000 (*.f64 x x) 238732414637843/250000000000000)
✓	0.2b	(.f64 x (fma.f64 -6450306886639899/50000000000000000 (.f64 x x) 238732414637843/250000000000000))

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(.f64 x (fma.f64 -6450306886639899/50000000000000000 (.f64 x x) 238732414637843/250000000000000))
2.0ms	(fma.f64 -6450306886639899/50000000000000000 (*.f64 x x) 238732414637843/250000000000000)

rewrite42.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

572×	`log1p-expm1-u_binary64`
572×	`expm1-log1p-u_binary64`
279×	`log-prod_binary64`
167×	`pow2_binary64`
118×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	142	19
2	1578	19

Stop Event

1×	node limit

Counts

2 → 52

Calls

2 calls:

41.0ms	(fma.f64 -6450306886639899/50000000000000000 (*.f64 x x) 238732414637843/250000000000000)
41.0ms	(.f64 x (fma.f64 -6450306886639899/50000000000000000 (.f64 x x) 238732414637843/250000000000000))

simplify41.0ms (2%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
419×	`fma-neg_binary64`
401×	`distribute-rgt-neg-in_binary64`
375×	`distribute-lft-neg-in_binary64`
243×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	240
1	41	222
2	96	204
3	287	204
4	906	204
5	1781	204
6	2961	204
7	4351	204

Stop Event

1×	node limit

Counts

76 → 62

prune42.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	62	9	71

Error

Counts

71 → 9

Alt Table

Status	Error	Program
✓	0.2b	(.f64 x (fma.f64 -6450306886639899/50000000000000000 (.f64 x x) 238732414637843/250000000000000))
✓	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	27.4b	(pow.f64 (sqrt.f64 (.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))) 2)
	41.8b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000) 3)))
	16.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))))
	1.4b	(pow.f64 (cbrt.f64 (.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))) 3)
	29.8b	(-.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 13606116089006033875034270860295875508316107/15625000000000000000000000000000000000000000)) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	28.7b	(-.f64 (.f64 238732414637843/250000000000000 x) (pow.f64 (.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3/2)) 2))

Compiler

Compiled 924 to 614 computations (33.5% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
✓	0.1b	(.f64 (.f64 x x) x)
✓	0.1b	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
	0.1b	(*.f64 238732414637843/250000000000000 x)

series10.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
3.0ms	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
2.0ms	(.f64 (.f64 x x) x)

rewrite65.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

459×	`log-prod_binary64`
403×	`fma-def_binary64`
211×	`egg-rr`
178×	`fma-neg_binary64`
166×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	204	22
2	2568	22

Stop Event

1×	node limit

Counts

3 → 211

Calls

3 calls:

62.0ms	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
62.0ms	(.f64 (.f64 x x) x)
62.0ms	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))

simplify37.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

818×	`unswap-sqr_binary64`
608×	`fma-def_binary64`
293×	`distribute-rgt-neg-in_binary64`
281×	`distribute-lft-neg-in_binary64`
249×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	267
1	27	249
2	68	249
3	205	249
4	456	249
5	1166	249
6	1902	249
7	2795	249

Stop Event

1×	node limit

Counts

247 → 218

prune202.0ms (10.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	235	8	243

Error

Counts

243 → 8

Alt Table

Status	Error	Program
	28.7b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 (pow.f64 x 3/2) 2)))
✓	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	27.4b	(pow.f64 (sqrt.f64 (.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))) 2)
	41.8b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000) 3)))
	16.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))))
	1.4b	(pow.f64 (cbrt.f64 (.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))) 3)
	29.8b	(-.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 13606116089006033875034270860295875508316107/15625000000000000000000000000000000000000000)) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))

Compiler

Compiled 4898 to 3783 computations (22.8% saved)

regimes135.0ms (6.8%)

Accuracy

Total 0.2b remaining (92.2%)

Threshold costs 0.2b (92.2%)

Counts

68 → 1

Compiler

Compiled 1528 to 1194 computations (21.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	12	14

Stop Event

1×

saturated

end110.0ms (5.5%)

Compiler: Compiled 117 to 90 computations (23.1% saved)

Details

analyze4.0ms (0.2%)

sample755.0ms (37.9%)

simplify39.0ms (2%)

prune3.0ms (0.2%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite49.0ms (2.5%)

simplify43.0ms (2.1%)

prune61.0ms (3.1%)

localize6.0ms (0.3%)

series7.0ms (0.4%)

rewrite62.0ms (3.1%)

simplify58.0ms (2.9%)

prune189.0ms (9.5%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite42.0ms (2.1%)

simplify41.0ms (2%)

prune42.0ms (2.1%)

localize6.0ms (0.3%)

series10.0ms (0.5%)

rewrite65.0ms (3.3%)

simplify37.0ms (1.9%)

prune202.0ms (10.2%)

regimes135.0ms (6.8%)

simplify2.0ms (0.1%)

end110.0ms (5.5%)

Profiling