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
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
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample767.0ms (41.5%)

Results

739.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	12	9

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

29.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	28.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

series5.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
2.0ms	(.f64 2 (.f64 x x))

rewrite40.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

466×	`log1p-expm1-u_binary64`
466×	`expm1-log1p-u_binary64`
441×	`unpow-prod-down_binary64`
268×	`log-prod_binary64`
138×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	122	13
2	1367	13

Stop Event

1×	node limit

Counts

2 → 71

Calls

2 calls:

39.0ms	(.f64 2 (.f64 x x))
39.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

simplify47.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
286×	`distribute-rgt-in_binary64`
242×	`unswap-sqr_binary64`
225×	`fma-neg_binary64`
201×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	164
1	20	164
2	43	164
3	83	164
4	203	164
5	607	164
6	959	164
7	1606	164
8	2009	164
9	2876	164
10	3703	164
11	4514	164

Stop Event

1×	node limit

Counts

95 → 75

prune47.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	67	8	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	9	76

Error

0.2b

Counts

76 → 9

Alt Table

Status	Error	Program
▶	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	41.0b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	31.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	46.7b	(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) 2) 1/2))
	31.4b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	29.2b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.8b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	31.7b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	29.6b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))

Compiler

Compiled 948 to 734 computations (22.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 x (sqrt.f64 2))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 x (sqrt.f64 2))

rewrite28.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
335×	`pow1_binary64`
247×	`unpow-prod-down_binary64`
204×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	100	6
2	1080	6

Stop Event

1×	node limit

Counts

1 → 33

Calls

1 calls:

27.0ms

(*.f64 x (sqrt.f64 2))

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

45 → 34

prune21.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	34	9	43

Error

0.1b

Counts

43 → 9

Alt Table

Status	Error	Program
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	41.0b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	43.6b	(fabs.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3)))
	31.8b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	31.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	31.7b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
▶	1.4b	(fabs.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3))
✓	29.2b	(sqrt.f64 (.f64 2 (.f64 x x)))
	29.6b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))

Compiler

Compiled 488 to 405 computations (17% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.5b	(*.f64 x (sqrt.f64 2))
✓	0.6b	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

series370.0ms (20%)

Counts

2 → 24

Calls

2 calls:

190.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
180.0ms	(cbrt.f64 (*.f64 x (sqrt.f64 2)))

rewrite41.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

542×	`log1p-expm1-u_binary64`
542×	`expm1-log1p-u_binary64`
492×	`unpow-prod-down_binary64`
278×	`log-prod_binary64`
155×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	161	14
2	1561	14

Stop Event

1×	node limit

Counts

2 → 110

Calls

2 calls:

39.0ms	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
39.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

simplify29.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

425×	`fma-def_binary64`
406×	`unswap-sqr_binary64`
271×	`associate-+l+_binary64`
225×	`associate-+r+_binary64`
155×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	448
1	74	448
2	163	424
3	443	220
4	1554	220

Stop Event

1×	node limit

Counts

134 → 119

prune83.0ms (4.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	4	2	6
Picked	1	0	1
Done	0	2	2
Total	153	9	162

Error

0.0b

Counts

162 → 9

Alt Table

Status	Error	Program
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	41.0b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	1.4b	(fabs.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
	1.5b	(fabs.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2) (pow.f64 (cbrt.f64 2) 3/2)))
	32.1b	(fabs.f64 (.f64 (pow.f64 (cbrt.f64 x) 3/2) (pow.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3/2)))
▶	0.5b	(fabs.f64 (.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x)))
	29.6b	(fabs.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (.f64 2 (.f64 x x))))))
	31.7b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
✓	29.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 2304 to 1893 computations (17.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 2 1/4) x)
✓	0.4b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

series30.0ms (1.6%)

Counts

2 → 12

Calls

2 calls:

27.0ms	(*.f64 (pow.f64 2 1/4) x)
3.0ms	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite31.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`log1p-expm1-u_binary64`
566×	`expm1-log1p-u_binary64`
311×	`log-prod_binary64`
168×	`pow2_binary64`
119×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	148	13
2	1623	13

Stop Event

1×	node limit

Counts

2 → 42

Calls

2 calls:

31.0ms	(*.f64 (pow.f64 2 1/4) x)
31.0ms	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

54 → 43

prune26.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	43	9	52

Error

0.0b

Counts

52 → 9

Alt Table

Status	Error	Program
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	41.0b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	1.4b	(fabs.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
	1.5b	(fabs.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2) (pow.f64 (cbrt.f64 2) 3/2)))
	32.1b	(fabs.f64 (.f64 (pow.f64 (cbrt.f64 x) 3/2) (pow.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3/2)))
✓	0.5b	(fabs.f64 (.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x)))
	29.6b	(fabs.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (.f64 2 (.f64 x x))))))
	31.7b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
✓	29.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 622 to 546 computations (12.2% saved)

regimes124.0ms (6.7%)

Accuracy

Total 0.4b remaining (94.8%)

Threshold costs 0.4b (94.8%)

Counts

32 → 1

Compiler

Compiled 1504 to 1254 computations (16.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`fabs-mul_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	11	8

Stop Event

1×

saturated

end110.0ms (5.9%)

Compiler: Compiled 115 to 94 computations (18.3% saved)

Details

analyze4.0ms (0.2%)

sample767.0ms (41.5%)

simplify6.0ms (0.3%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series5.0ms (0.3%)

rewrite40.0ms (2.2%)

simplify47.0ms (2.6%)

prune47.0ms (2.5%)

localize3.0ms (0.2%)

series3.0ms (0.1%)

rewrite28.0ms (1.5%)

simplify7.0ms (0.4%)

prune21.0ms (1.1%)

localize10.0ms (0.5%)

series370.0ms (20%)

rewrite41.0ms (2.2%)

simplify29.0ms (1.6%)

prune83.0ms (4.5%)

localize5.0ms (0.3%)

series30.0ms (1.6%)

rewrite31.0ms (1.7%)

simplify7.0ms (0.4%)

prune26.0ms (1.4%)

regimes124.0ms (6.7%)

simplify2.0ms (0.1%)

end110.0ms (5.9%)

Profiling