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

Compiler

Compiled 8 to 6 computations (25% saved)

sample789.0ms (17.6%)

Results

765.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9
3	11	9

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

32.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	31.6b	(sqrt.f64 (.f64 (.f64 2 x) x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite38.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

488×	`log1p-expm1-u_binary64`
488×	`expm1-log1p-u_binary64`
483×	`unpow-prod-down_binary64`
289×	`log-prod_binary64`
142×	`pow2_binary64`

Counts

1 → 55

Calls

1 calls:

37.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	121	6
2	1317	6
3	4961	6
0	0	0
1	0	0

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Counts

67 → 57

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	24	80
3	25	80
4	29	80
5	47	80
6	58	80
7	63	80
8	75	80
9	72	80
10	58	80

prune33.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	51	6	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	7	58

Error

0.1b

Counts

58 → 7

Alt Table

Status	Error	Program
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	17.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
▶	17.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	29.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	29.4b	(*.f64 (sqrt.f64 2) x)
✓	32.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 768 to 509 computations (33.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
✓	0.5b	(pow.f64 (cbrt.f64 x) 2)
✓	0.6b	(cbrt.f64 x)
✓	16.5b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

series1.4s (30.2%)

Counts

4 → 48

Calls

4 calls:

1.1s	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
157.0ms	(cbrt.f64 x)
43.0ms	(pow.f64 (cbrt.f64 x) 2)
16.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

rewrite64.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

824×	`log1p-expm1-u_binary64`
824×	`expm1-log1p-u_binary64`
499×	`prod-diff_binary64`
99×	`add-sqr-sqrt_binary64`
93×	`add-cube-cbrt_binary64`

Counts

4 → 80

Calls

4 calls:

62.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
62.0ms	(pow.f64 (cbrt.f64 x) 2)
62.0ms	(cbrt.f64 x)
62.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	219	25
2	2178	25
3	5792	25
0	0	0
1	0	0

simplify138.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

927×	`fma-def_binary64`
735×	`sqr-pow_binary64`
412×	`unswap-sqr_binary64`
388×	`*-commutative_binary64`
288×	`fma-neg_binary64`

Counts

128 → 93

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	400
1	53	400
2	100	400
3	234	400
4	671	400
5	1071	400
6	1134	400
7	1347	400
8	1640	400
9	1962	400
10	2318	400
11	2672	400
12	3136	400
13	3857	400
14	4627	400
15	4938	400
16	4746	400

prune56.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	121	8	129

Error

0.1b

Counts

129 → 8

Alt Table

Status	Error	Program
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	17.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	29.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	29.4b	(*.f64 (sqrt.f64 2) x)
	17.7b	(.f64 (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
▶	17.5b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2))
✓	32.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 2076 to 1229 computations (40.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 (cbrt.f64 x))
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)
✓	16.5b	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2)

series1.5s (32.4%)

Counts

3 → 36

Calls

3 calls:

918.0ms	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2)
283.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)
253.0ms	(cbrt.f64 (cbrt.f64 x))

rewrite54.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

772×	`log1p-expm1-u_binary64`
772×	`expm1-log1p-u_binary64`
664×	`prod-diff_binary64`
90×	`add-sqr-sqrt_binary64`
85×	`add-cbrt-cube_binary64`

Counts

3 → 67

Calls

3 calls:

53.0ms	(cbrt.f64 (cbrt.f64 x))
53.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)
53.0ms	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	201	16
2	2034	16
3	5765	16
0	0	0
1	0	0

simplify110.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1015×	`fma-def_binary64`
790×	`sqr-pow_binary64`
323×	`cube-prod_binary64`
322×	`*-commutative_binary64`
312×	`unswap-sqr_binary64`

Counts

103 → 76

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	300
1	55	300
2	104	300
3	224	300
4	598	300
5	908	300
6	987	300
7	1200	300
8	1489	300
9	1842	300
10	2269	300
11	2720	300
12	3222	300
13	4053	300
14	4559	300
15	4839	300

prune70.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	134	8	142

Error

0.1b

Counts

142 → 8

Alt Table

Status	Error	Program
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	17.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	29.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	29.4b	(*.f64 (sqrt.f64 2) x)
▶	17.7b	(.f64 (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
✓	17.5b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2))
✓	32.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 2764 to 1799 computations (34.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 x)
	0.6b	(cbrt.f64 (cbrt.f64 x))
	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)
	16.5b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

prune75.0ms (1.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	134	8	142

Error

0.1b

Counts

142 → 8

Alt Table

Status	Error	Program
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	17.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	29.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	29.4b	(*.f64 (sqrt.f64 2) x)
✓	17.7b	(.f64 (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
✓	17.5b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2))
✓	32.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 2791 to 1732 computations (37.9% saved)

regimes72.0ms (1.6%)

Accuracy

Total 0.3b remaining (69.3%)

Threshold costs 0.3b (69.3%)

Counts

20 → 2

Compiler

Compiled 777 to 548 computations (29.5% saved)

bsearch16.0ms (0.4%)

Steps

Iters	Range		Point
9	-7.0290898584775714e-304	1.0895490308086033e-304	6.07190567874543e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	24	25
2	32	25
3	37	25
4	39	25
5	39	25

end94.0ms (2.1%)

Compiler: Compiled 119 to 86 computations (27.7% saved)

Details

analyze4.0ms (0.1%)

sample789.0ms (17.6%)

simplify9.0ms (0.2%)

prune2.0ms (0%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite38.0ms (0.8%)

simplify12.0ms (0.3%)

prune33.0ms (0.7%)

localize10.0ms (0.2%)

series1.4s (30.2%)

rewrite64.0ms (1.4%)

simplify138.0ms (3.1%)

prune56.0ms (1.2%)

localize14.0ms (0.3%)

series1.5s (32.4%)

rewrite54.0ms (1.2%)

simplify110.0ms (2.4%)

prune70.0ms (1.6%)

localize13.0ms (0.3%)

prune75.0ms (1.7%)

regimes72.0ms (1.6%)

bsearch16.0ms (0.4%)

simplify3.0ms (0.1%)

end94.0ms (2.1%)

Profiling