Details

analyze20.0ms (0.7%)

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)

sample15.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% 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

prune2.0ms (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)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite41.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`flip3-+_binary64`
12×	`pow1_binary64`

Counts

3 → 131

Calls

3 calls:

13.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
12.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
10.0ms	(sqrt.f64 (+.f64 x 1))

series52.0ms (1.7%)

Counts

3 → 12

Calls

3 calls:

41.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(sqrt.f64 (+.f64 x 1))

simplify106.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-neg_binary64`
494×	`associate-/l*_binary64`
494×	`fma-def_binary64`
271×	`associate-/r*_binary64`
170×	`associate-*l/_binary64`

Counts

143 → 203

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	1601
1	315	1465
2	1033	1443
3	3945	1430
4	4927	1430
5	5069	1430

prune140.0ms (4.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	201	3	204

Error

Counts

204 → 3

Alt Table

Status	Error	Program
	41.1b	(/.f64 x (-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))
	6.0b	(+.f64 (.f64 (.f64 1 1) (/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))) (.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (*.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))))
▶	1.6b	(/.f64 x (+.f64 1 (exp.f64 (*.f64 1/2 (log1p.f64 x)))))

Compiler

Compiled 2690 to 2133 computations (20.7% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 (*.f64 1/2 (log1p.f64 x))))
✓	0.2b	(/.f64 x (+.f64 1 (exp.f64 (*.f64 1/2 (log1p.f64 x)))))
✓	1.6b	(exp.f64 (*.f64 1/2 (log1p.f64 x)))

rewrite42.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cube-cbrt_binary64`
15×	`add-log-exp_binary64`
13×	`add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`

Counts

3 → 120

Calls

3 calls:

14.0ms	(+.f64 1 (exp.f64 (*.f64 1/2 (log1p.f64 x))))
12.0ms	(/.f64 x (+.f64 1 (exp.f64 (*.f64 1/2 (log1p.f64 x)))))
10.0ms	(exp.f64 (*.f64 1/2 (log1p.f64 x)))

series33.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

23.0ms	(/.f64 x (+.f64 1 (exp.f64 (*.f64 1/2 (log1p.f64 x)))))
5.0ms	(exp.f64 (*.f64 1/2 (log1p.f64 x)))
5.0ms	(+.f64 1 (exp.f64 (*.f64 1/2 (log1p.f64 x))))

simplify121.0ms (4%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
285×	`fma-neg_binary64`
234×	`distribute-rgt-in_binary64`
214×	`distribute-lft-in_binary64`
202×	`cancel-sign-sub-inv_binary64`

Counts

156 → 256

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	3263
1	628	3045
2	2028	2220
3	4698	2209
4	4933	2209

prune165.0ms (5.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	256	3	259

Error

Counts

259 → 3

Alt Table

Status	Error	Program
	41.1b	(/.f64 x (-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))
▶	6.0b	(+.f64 (.f64 (.f64 1 1) (/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))) (.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (*.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))))
✓	1.6b	(/.f64 x (+.f64 1 (exp.f64 (*.f64 1/2 (log1p.f64 x)))))

Compiler

Compiled 4413 to 3185 computations (27.8% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
✓	4.3b	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
	5.9b	(/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
✓	5.9b	(/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))

rewrite56.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cube-cbrt_binary64`
26×	`flip3-+_binary64`
22×	`sqrt-div_binary64`
14×	`add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`

Counts

3 → 148

Calls

3 calls:

20.0ms	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
14.0ms	(/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
13.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)

series43.0ms (1.4%)

Counts

3 → 14

Calls

3 calls:

23.0ms	(/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
15.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
5.0ms	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify145.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1214×	`fma-neg_binary64`
344×	`cancel-sign-sub-inv_binary64`
302×	`unswap-sqr_binary64`
241×	`log-prod_binary64`
218×	`exp-prod_binary64`

Counts

162 → 264

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	209	2429
1	490	2215
2	2037	2094
3	3735	2076
4	4966	2076
5	5044	2076

prune434.0ms (14.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	351	3	354

Error

Counts

354 → 3

Alt Table

Status	Error	Program
▶	41.1b	(/.f64 x (-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))
✓	6.0b	(+.f64 (.f64 (.f64 1 1) (/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))) (.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (*.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))))
✓	1.6b	(/.f64 x (+.f64 1 (exp.f64 (*.f64 1/2 (log1p.f64 x)))))

Compiler

Compiled 15588 to 13071 computations (16.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	3.3b	(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
	4.2b	(-.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	4.2b	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite62.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-log-exp_binary64`
13×	`add-cbrt-cube_binary64`
12×	`pow1_binary64`

Counts

3 → 143

Calls

3 calls:

18.0ms	(/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1))))
18.0ms	(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
16.0ms	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

series99.0ms (3.2%)

Counts

3 → 12

Calls

3 calls:

55.0ms	(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
36.0ms	(/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify129.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1005×	`fma-neg_binary64`
497×	`cancel-sign-sub-inv_binary64`
256×	`distribute-rgt-neg-in_binary64`
231×	`log-prod_binary64`
208×	`distribute-lft-neg-in_binary64`

Counts

155 → 235

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	3418
1	569	3103
2	2256	2350
3	3991	2346
4	4784	2346

prune226.0ms (7.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	308	0	308
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	308	3	311

Error

Counts

311 → 3

Alt Table

Status	Error	Program
✓	41.1b	(/.f64 x (-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))
✓	6.0b	(+.f64 (.f64 (.f64 1 1) (/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))) (.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (*.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 x (+.f64 (pow.f64 1 3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))))
✓	1.6b	(/.f64 x (+.f64 1 (exp.f64 (*.f64 1/2 (log1p.f64 x)))))

Compiler

Compiled 9707 to 8053 computations (17% saved)

regimes551.0ms (18%)

Accuracy

Total 0.2b remaining (95.5%)

Threshold costs 0.2b (95.5%)

Compiler

Compiled 9842 to 8010 computations (18.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	12
2	12	12

end0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample525.0ms (17.2%)

Algorithm

1×

intervals

Results

286.0ms	7998×	body	128	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 99 to 82 computations (17.2% saved)

Details

analyze20.0ms (0.7%)

sample15.0ms (0.5%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite41.0ms (1.3%)

series52.0ms (1.7%)

simplify106.0ms (3.5%)

prune140.0ms (4.6%)

localize8.0ms (0.3%)

rewrite42.0ms (1.4%)

series33.0ms (1.1%)

simplify121.0ms (4%)

prune165.0ms (5.4%)

localize15.0ms (0.5%)

rewrite56.0ms (1.8%)

series43.0ms (1.4%)

simplify145.0ms (4.8%)

prune434.0ms (14.2%)

localize8.0ms (0.3%)

rewrite62.0ms (2%)

series99.0ms (3.2%)

simplify129.0ms (4.2%)

prune226.0ms (7.4%)

regimes551.0ms (18%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample525.0ms (17.2%)

Profiling