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)

sample685.0ms (17.4%)

Results

658.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (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

29.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.2b	(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))

rewrite41.0ms (1.1%)

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:

40.0ms

(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

prune34.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	49	8	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	9	58

Error

0.1b

Counts

58 → 9

Alt Table

Status	Error	Program
	34.6b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	41.2b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x x))) (pow.f64 (.f64 (sqrt.f64 (+.f64 x x)) x) 1/2))
	41.1b	(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 (sqrt.f64 x) (+.f64 x x)) 1/2))
▶	12.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	12.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	34.4b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	29.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.7b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 824 to 541 computations (34.3% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
✓	0.5b	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
✓	0.6b	(cbrt.f64 (+.f64 x x))
✓	11.4b	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)

series985.0ms (25%)

Counts

4 → 48

Calls

4 calls:

877.0ms	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)
51.0ms	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
34.0ms	(cbrt.f64 (+.f64 x x))
22.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))

rewrite85.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
308×	`log-prod_binary64`
238×	`prod-diff_binary64`
218×	`egg-rr`

Counts

4 → 218

Calls

4 calls:

80.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
80.0ms	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
80.0ms	(cbrt.f64 (+.f64 x x))
80.0ms	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	215	26
2	1624	26
3	4958	26
0	0	0
1	0	0

simplify120.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-def_binary64`
790×	`unswap-sqr_binary64`
662×	`sqr-pow_binary64`
468×	`*-commutative_binary64`
344×	`distribute-rgt-in_binary64`

Counts

266 → 139

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	516
1	64	516
2	129	516
3	324	516
4	1021	516
5	1715	516
6	1918	516
7	2288	516
8	2999	516
9	3608	516
10	4272	516
11	4564	516
12	4655	516

prune101.0ms (2.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	231	2	233
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	232	10	242

Error

0.1b

Counts

242 → 10

Alt Table

Status	Error	Program
▶	12.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	29.5b	(pow.f64 (pow.f64 (*.f64 x (+.f64 x x)) 1/4) 2)
	34.6b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	41.2b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x x))) (pow.f64 (.f64 (sqrt.f64 (+.f64 x x)) x) 1/2))
✓	12.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	12.2b	(.f64 (sqrt.f64 (pow.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) 2)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	34.4b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	29.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.7b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 5009 to 2291 computations (54.3% saved)

localize10.0ms (0.3%)

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)
✓	11.4b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)

series890.0ms (22.6%)

Counts

4 → 48

Calls

4 calls:

802.0ms	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
41.0ms	(pow.f64 (cbrt.f64 x) 2)
31.0ms	(cbrt.f64 x)
16.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

rewrite65.0ms (1.7%)

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 → 83

Calls

4 calls:

63.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
63.0ms	(pow.f64 (cbrt.f64 x) 2)
63.0ms	(cbrt.f64 x)
63.0ms	(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	28
2	2178	28
3	5792	28
0	0	0
1	0	0

simplify143.0ms (3.6%)

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

131 → 95

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

prune70.0ms (1.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	122	12	134

Error

0.1b

Counts

134 → 12

Alt Table

Status	Error	Program
	12.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)) (+.f64 x x)) 1/2))
	41.2b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x x))) (pow.f64 (.f64 (sqrt.f64 (+.f64 x x)) x) 1/2))
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	12.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/4)))
▶	11.9b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	34.6b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	12.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	29.5b	(pow.f64 (pow.f64 (*.f64 x (+.f64 x x)) 1/4) 2)
	34.4b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	12.6b	(.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))
	29.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.7b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 2295 to 1205 computations (47.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	0.6b	(cbrt.f64 x)
	11.4b	(pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2)
✓	11.4b	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

series122.0ms (3.1%)

Counts

2 → 24

Calls

2 calls:

80.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
42.0ms	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

rewrite51.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

918×	`prod-diff_binary64`
832×	`expm1-log1p-u_binary64`
107×	`add-sqr-sqrt_binary64`
103×	`log1p-expm1-u_binary64`
99×	`add-cube-cbrt_binary64`

Counts

2 → 45

Calls

2 calls:

50.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
50.0ms	(sqrt.f64 (*.f64 x (cbrt.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	230	15
2	2236	15
3	5175	15
0	0	0
1	0	0

simplify120.0ms (3%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-def_binary64`
531×	`associate-l_binary64`
478×	`sqr-pow_binary64`
474×	`unswap-sqr_binary64`
289×	`associate-r_binary64`

Counts

69 → 52

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	288
1	47	288
2	92	288
3	174	288
4	385	288
5	1056	288
6	1695	288
7	2280	288
8	2955	288
9	3564	288
10	4112	288
11	4714	288
12	4996	288
13	4691	288

prune67.0ms (1.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	4	5	9
Picked	0	1	1
Done	0	2	2
Total	136	10	146

Error

0.1b

Counts

146 → 10

Alt Table

Status	Error	Program
	12.0b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	11.9b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	41.2b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x x))) (pow.f64 (.f64 (sqrt.f64 (+.f64 x x)) x) 1/2))
✓	12.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	29.5b	(pow.f64 (pow.f64 (*.f64 x (+.f64 x x)) 1/4) 2)
	34.4b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	12.2b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 x)))) (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 x x)) 1/2))
	29.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.7b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 2407 to 1047 computations (56.5% saved)

regimes148.0ms (3.8%)

Accuracy

Total 0.3b remaining (74%)

Threshold costs 0.3b (74%)

Counts

46 → 2

Compiler

Compiled 2211 to 1514 computations (31.5% saved)

bsearch17.0ms (0.4%)

Steps

Iters	Range		Point
9	-3.081099170909963e-308	1.0738827390072638e-303	-1.5649434706456e-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

end118.0ms (3%)

Compiler: Compiled 156 to 104 computations (33.3% saved)

Details

analyze4.0ms (0.1%)

sample685.0ms (17.4%)

simplify6.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series3.0ms (0.1%)

rewrite41.0ms (1.1%)

simplify12.0ms (0.3%)

prune34.0ms (0.9%)

localize15.0ms (0.4%)

series985.0ms (25%)

rewrite85.0ms (2.2%)

simplify120.0ms (3%)

prune101.0ms (2.6%)

localize10.0ms (0.3%)

series890.0ms (22.6%)

rewrite65.0ms (1.7%)

simplify143.0ms (3.6%)

prune70.0ms (1.8%)

localize13.0ms (0.3%)

series122.0ms (3.1%)

rewrite51.0ms (1.3%)

simplify120.0ms (3%)

prune67.0ms (1.7%)

regimes148.0ms (3.8%)

bsearch17.0ms (0.4%)

simplify3.0ms (0.1%)

end118.0ms (3%)

Profiling