Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample950.0ms (24.9%)

Results

914.0ms	8252×	body	128	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

prune3.0ms (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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series112.0ms (2.9%)

Counts

3 → 12

Calls

3 calls:

81.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
16.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
14.0ms	(sqrt.f64 (+.f64 x 1))

rewrite37.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

13.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(sqrt.f64 (+.f64 x 1))

simplify172.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
333×	`associate-/r*_binary64`
321×	`associate-/l/_binary64`
303×	`associate-*l/_binary64`
284×	`cancel-sign-sub-inv_binary64`

Counts

94 → 108

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	1335
1	263	1239
2	634	1227
3	1878	1212
4	4323	1211
5	4987	1211
6	4875	1211

prune164.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	5	109

Error

Counts

109 → 5

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	0.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
	1.6b	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
	21.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	21.4b	(fma.f64 1/2 x (.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)))

Compiler

Compiled 1653 to 1266 computations (23.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
✓	0.2b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

series110.0ms (2.9%)

Counts

2 → 8

Calls

2 calls:

88.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
22.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)

rewrite65.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`*-un-lft-identity_binary64`
156×	`times-frac_binary64`
108×	`add-sqr-sqrt_binary64`
76×	`add-cube-cbrt_binary64`
64×	`distribute-lft-out_binary64`

Counts

2 → 157

Calls

2 calls:

21.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
12.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)

simplify248.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-neg_binary64`
842×	`fma-def_binary64`
286×	`times-frac_binary64`
250×	`*-commutative_binary64`
241×	`distribute-rgt-in_binary64`

Counts

165 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	3593
1	290	3208
2	750	3139
3	2088	3123
4	4240	3123
5	4979	3123
6	4918	3123

prune315.0ms (8.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	236	5	241

Error

Counts

241 → 5

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
▶	1.6b	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
	21.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	21.4b	(fma.f64 1/2 x (.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)))

Compiler

Compiled 4503 to 3553 computations (21.1% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	0.0b	(sqrt.f64 (+.f64 x 1))
	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	1.6b	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))

series591.0ms (15.5%)

Counts

2 → 8

Calls

2 calls:

512.0ms	(log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
78.0ms	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))

simplify100.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

598×	`distribute-rgt-neg-in_binary64`
542×	`fma-def_binary64`
489×	`distribute-lft-neg-in_binary64`
403×	`cancel-sign-sub-inv_binary64`
382×	`associate-l_binary64`

Counts

30 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	515
1	121	453
2	289	444
3	843	426
4	2968	426
5	4812	426
6	5111	426

prune182.0ms (4.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	122	5	127

Error

Counts

127 → 5

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
✓	1.6b	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
	21.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶	21.4b	(fma.f64 1/2 x (.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)))

Compiler

Compiled 2046 to 1618 computations (20.9% saved)

localize14.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)
✓	0.0b	(.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8))
3.0ms	(fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`

Counts

2 → 33

Calls

2 calls:

5.0ms	(.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8))
0.0ms	(fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)

simplify159.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-def_binary64`
557×	`fma-neg_binary64`
551×	`associate-l_binary64`
446×	`exp-prod_binary64`
423×	`associate-r_binary64`

Counts

57 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	1059
1	179	872
2	515	755
3	1871	755
4	3945	755
5	4954	755
6	4930	755

prune103.0ms (2.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	71	5	76

Error

Counts

76 → 5

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
✓	1.6b	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
	21.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	21.4b	(fma.f64 1/2 x (.f64 (.f64 x x) (fma.f64 x (-.f64 1/16 (*.f64 5/128 x)) -1/8)))

Compiler

Compiled 1455 to 964 computations (33.7% saved)

regimes276.0ms (7.2%)

Accuracy

Total 0.2b remaining (98.1%)

Threshold costs 0.2b (98.1%)

Counts

79 → 1

Compiler

Compiled 2018 to 1572 computations (22.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

end148.0ms (3.9%)

Compiler: Compiled 78 to 59 computations (24.4% saved)

Details

analyze3.0ms (0.1%)

sample950.0ms (24.9%)

simplify10.0ms (0.3%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series112.0ms (2.9%)

rewrite37.0ms (1%)

simplify172.0ms (4.5%)

prune164.0ms (4.3%)

localize12.0ms (0.3%)

series110.0ms (2.9%)

rewrite65.0ms (1.7%)

simplify248.0ms (6.5%)

prune315.0ms (8.2%)

localize17.0ms (0.4%)

series591.0ms (15.5%)

rewrite1.0ms (0%)

simplify100.0ms (2.6%)

prune182.0ms (4.8%)

localize14.0ms (0.4%)

series7.0ms (0.2%)

rewrite7.0ms (0.2%)

simplify159.0ms (4.2%)

prune103.0ms (2.7%)

regimes276.0ms (7.2%)

simplify4.0ms (0.1%)

end148.0ms (3.9%)

Profiling