Details

analyze551.0ms (13.1%)

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)

sample52.0ms (1.2%)

Algorithm

1×

intervals

Results

24.0ms	84×	body	1024	valid
8.0ms	49×	body	512	valid
4.0ms	95×	body	128	valid
3.0ms	6×	body	2048	valid
2.0ms	22×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify83.0ms (2%)

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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 18 to 15 computations (16.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.2b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

4×	`*-un-lft-identity_binary64`
4×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`sqrt-div_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 16

Calls

1 calls:

5.0ms

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

Compiler

Compiled 168 to 116 computations (31% saved)

series35.0ms (0.8%)

Error

0.2b

Counts

1 → 6

Calls

1 calls:

27.0ms

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

Compiler

Compiled 234 to 209 computations (10.7% saved)

simplify61.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
661×	`associate-/l*_binary64`
338×	`associate-/r*_binary64`
177×	`associate-/r/_binary64`
153×	`distribute-neg-frac_binary64`

Counts

22 → 15

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	361
1	167	350
2	439	322
3	1654	316
4	4922	316
5	4948	316

prune24.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Error

0.2b

Counts

16 → 4

Alt Table

Status	Error	Program
✓	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
	0.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))
	21.1b	(-.f64 (+.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 x (sqrt.f64 2))) (.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (pow.f64 x 3) (-.f64 (/.f64 1/16 (sqrt.f64 2)) (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)))))

Compiler

Compiled 323 to 262 computations (18.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(sqrt.f64 (+.f64 (exp.f64 x) 1))
0.2b	(sqrt.f64 (+.f64 (exp.f64 x) 1))
0.7b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))

rewrite129.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

98×	`sqrt-prod_binary64`
65×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
34×	`sqrt-pow1_binary64`
28×	`sqrt-div_binary64`

Counts

3 → 128

Calls

3 calls:

18.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
4.0ms	(sqrt.f64 (+.f64 (exp.f64 x) 1))
4.0ms	(sqrt.f64 (+.f64 (exp.f64 x) 1))

Compiler

Compiled 1886 to 1360 computations (27.9% saved)

series59.0ms (1.4%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

14.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
14.0ms	(sqrt.f64 (+.f64 (exp.f64 x) 1))
13.0ms	(sqrt.f64 (+.f64 (exp.f64 x) 1))

Compiler

Compiled 895 to 778 computations (13.1% saved)

simplify168.0ms (4%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
296×	`associate-l_binary64`
236×	`associate-r_binary64`
153×	`distribute-neg-frac_binary64`
147×	`distribute-rgt-out_binary64`

Counts

146 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	126	2317
1	242	2163
2	681	2046
3	2394	1986
4	4920	1975
5	4940	1975
6	4951	1975

prune62.0ms (1.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	112	4	116

Error

0.2b

Counts

116 → 4

Alt Table

Status	Error	Program
	21.1b	(+.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))
✓	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
▶	0.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))

Compiler

Compiled 1127 to 871 computations (22.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(sqrt.f64 (+.f64 (exp.f64 x) 1))
0.7b	(pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3)
0.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))

rewrite74.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

24×	`*-un-lft-identity_binary64`
20×	`sqrt-prod_binary64`
20×	`cbrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`cube-prod_binary64`

Counts

3 → 83

Calls

3 calls:

6.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))
6.0ms	(pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3)
4.0ms	(sqrt.f64 (+.f64 (exp.f64 x) 1))

Compiler

Compiled 964 to 736 computations (23.7% saved)

series60.0ms (1.4%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

18.0ms	(pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3)
13.0ms	(sqrt.f64 (+.f64 (exp.f64 x) 1))
12.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))

Compiler

Compiled 761 to 684 computations (10.1% saved)

simplify118.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

587×	`associate-l_binary64`
473×	`associate-r_binary64`
339×	`log-prod_binary64`
306×	`associate-+l+_binary64`
253×	`unswap-sqr_binary64`

Counts

101 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1596
1	340	1551
2	989	1441
3	4104	1431
4	4768	1431
5	4957	1431

prune35.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	78	4	82

Error

0.2b

Counts

82 → 4

Alt Table

Status	Error	Program
▶	21.1b	(+.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))
✓	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
✓	0.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))

Compiler

Compiled 660 to 532 computations (19.4% saved)

localize26.0ms (0.6%)

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)
9.3b	(+.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))
13.1b	(+.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))

rewrite370.0ms (8.8%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

30×	`times-frac_binary64`
30×	`unpow-prod-down_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`

Counts

4 → 119

Calls

4 calls:

19.0ms	(+.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))
15.0ms	(+.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)

series71.0ms (1.7%)

Error

0.2b

Counts

4 → 16

Calls

4 calls:

29.0ms	(+.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))
27.0ms	(+.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))
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)

simplify206.0ms (4.9%)

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

prune159.0ms (3.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	96	4	100

Error

0.2b

Counts

100 → 4

Alt Table

Status	Error	Program
	21.1b	(+.f64 (exp.f64 (log.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))))) (.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
	0.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))

Compiler

Compiled 4485 to 4054 computations (9.6% saved)

regimes221.0ms (5.3%)

Accuracy

Total 0.0b remaining (15.9%)

Threshold costs 0.0b (15.9%)

Compiler

Compiled 3814 to 3441 computations (9.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_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 (37.7%)

Algorithm

1×

intervals

Results

729.0ms	2555×	body	1024	valid
202.0ms	1290×	body	512	valid
138.0ms	3174×	body	128	valid
100.0ms	297×	body	2048	valid
69.0ms	684×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 91 to 79 computations (13.2% saved)

Details

analyze551.0ms (13.1%)

sample52.0ms (1.2%)

simplify83.0ms (2%)

prune8.0ms (0.2%)

localize5.0ms (0.1%)

rewrite19.0ms (0.5%)

series35.0ms (0.8%)

simplify61.0ms (1.5%)

prune24.0ms (0.6%)

localize6.0ms (0.1%)

rewrite129.0ms (3.1%)

series59.0ms (1.4%)

simplify168.0ms (4%)

prune62.0ms (1.5%)

localize6.0ms (0.2%)

rewrite74.0ms (1.8%)

series60.0ms (1.4%)

simplify118.0ms (2.8%)

prune35.0ms (0.8%)

localize26.0ms (0.6%)

rewrite370.0ms (8.8%)

series71.0ms (1.7%)

simplify206.0ms (4.9%)

prune159.0ms (3.8%)

regimes221.0ms (5.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.6s (37.7%)

Profiling