Details

analyze755.0ms (20.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample58.0ms (1.6%)

Algorithm

1×

intervals

Results

24.0ms	84×	body	1024	valid
8.0ms	92×	body	128	valid
8.0ms	50×	body	512	valid
4.0ms	10×	body	2048	valid
2.0ms	20×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify78.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

669×	`div-sub_binary64`
601×	`associate-/l*_binary64`
488×	`associate-/r*_binary64`
279×	`distribute-rgt-in_binary64`
273×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	32	19
3	55	19
4	116	11
5	296	8
6	987	8
7	4260	8
8	4954	8
9	5000	8
10	4831	8

prune8.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 18 to 15 computations (16.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

7×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64`
2×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `sqrt-div_binary64` `flip-+_binary64` `distribute-lft-out_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 28

Calls

2 calls:

5.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
3.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 294 to 198 computations (32.7% saved)

series39.0ms (1.1%)

Error

Counts

2 → 12

Calls

2 calls:

22.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
6.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 324 to 283 computations (12.7% saved)

simplify49.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
663×	`associate-/l*_binary64`
177×	`associate-/r/_binary64`
161×	`associate-+l+_binary64`
153×	`distribute-neg-frac_binary64`

Counts

40 → 27

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	545
1	211	521
2	543	490
3	1892	484
4	5073	484

prune28.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Error

Counts

28 → 2

Alt Table

Status	Error	Program
▶	19.7b	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Status

Error

Program

▶

19.7b

(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))

✓

0.0b

(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 393 to 304 computations (22.6% saved)

localize27.0ms (0.7%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))
1.6b	(pow.f64 (sqrt.f64 2) 5)
11.6b	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
13.6b	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))

rewrite384.0ms (10.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

30×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `unpow-prod-down_binary64` `times-frac_binary64`
27×	`add-log-exp_binary64`
22×	`associate-*l/_binary64`
18×	`frac-add_binary64`
16×	`sum-log_binary64`

Counts

4 → 119

Calls

4 calls:

18.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
14.0ms	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
6.0ms	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))
3.0ms	(pow.f64 (sqrt.f64 2) 5)

Compiler

Compiled 7774 to 7012 computations (9.8% saved)

series76.0ms (2.1%)

Error

Counts

4 → 16

Calls

4 calls:

29.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
28.0ms	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
0.0ms	(pow.f64 (sqrt.f64 2) 5)
0.0ms	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))

Compiler

Compiled 883 to 797 computations (9.7% saved)

simplify196.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

356×	`cancel-sign-sub-inv_binary64`
319×	`times-frac_binary64`
255×	`associate-r_binary64`
244×	`associate-l_binary64`
172×	`distribute-rgt-in_binary64`

Counts

135 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	282	6837
1	745	6277
2	3026	6235
3	4841	6235
4	4901	6235

prune164.0ms (4.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	96	2	98

Error

Counts

98 → 2

Alt Table

Status	Error	Program
	19.7b	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Status

Error

Program

19.7b

(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))

0.0b

(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 4465 to 4037 computations (9.6% saved)

regimes185.0ms (5%)

Accuracy

Total 0.0b remaining (7.9%)

Threshold costs 0.0b (7.9%)

Compiler

Compiled 2491 to 2142 computations (14% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	9	8
2	8	8

end1.0ms (0%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

sample1.6s (43.3%)

Algorithm

1×

intervals

Results

767.0ms	2730×	body	1024	valid
211.0ms	1338×	body	512	valid
137.0ms	3040×	body	128	valid
93.0ms	263×	body	2048	valid
64.0ms	629×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 71 to 62 computations (12.7% saved)

Details

analyze755.0ms (20.5%)

sample58.0ms (1.6%)

simplify78.0ms (2.1%)

prune8.0ms (0.2%)

localize5.0ms (0.1%)

rewrite38.0ms (1%)

series39.0ms (1.1%)

simplify49.0ms (1.3%)

prune28.0ms (0.8%)

localize27.0ms (0.7%)

rewrite384.0ms (10.4%)

series76.0ms (2.1%)

simplify196.0ms (5.3%)

prune164.0ms (4.4%)

regimes185.0ms (5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.6s (43.3%)

Profiling