Details

analyze1.2s (7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
49.8%	49.8%	0.4%	7
49.8%	49.8%	0.4%	8
49.8%	49.8%	0.4%	9
49.8%	49.8%	0.4%	10
49.8%	49.8%	0.4%	11
49.8%	49.8%	0.4%	12
49.8%	49.8%	0.4%	13
49.8%	49.8%	0.4%	14

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample2.0s (11.6%)

Symmetry

(sort Ev EAccept)

Results

1.8s	8255×	body	128	valid
1.0ms	1×	body	8192	exit
0.0ms	1×	body	256	valid

Compiler

Compiled 122 to 86 computations (29.5% saved)

simplify94.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

713×	`div-sub_binary64`
583×	`exp-sum_binary64`
502×	`exp-diff_binary64`
464×	`exp-prod_binary64`
370×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	46
1	57	46
2	158	44
3	433	44
4	1039	44
5	2185	44
6	3700	44
7	4917	44
8	4999	44
9	4971	44
10	5079	44

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))

Compiler

Compiled 145 to 95 computations (34.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)
✓	0.0b	(exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))
✓	0.0b	(/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)
✓	0.0b	(exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))

series219.0ms (1.3%)

Counts

4 → 240

Calls

4 calls:

81.0ms	(exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))
64.0ms	(exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))
49.0ms	(/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)
25.0ms	(/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)

rewrite54.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

176×	`*-un-lft-identity_binary64`
84×	`times-frac_binary64`
78×	`add-sqr-sqrt_binary64`
63×	`distribute-lft-out--_binary64`
50×	`exp-prod_binary64`

Counts

4 → 168

Calls

4 calls:

10.0ms	(exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))
9.0ms	(exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))
9.0ms	(/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)
9.0ms	(/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)

simplify187.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

613×	`times-frac_binary64`
453×	`fma-def_binary64`
408×	`associate-/l*_binary64`
354×	`associate-/r*_binary64`
217×	`+-commutative_binary64`

Counts

408 → 333

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	718	10869
1	2041	10609
2	5051	10609

prune375.0ms (2.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	331	2	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	332	2	334

Error

0.0b

Counts

334 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)))) (/.f64 NaChar (+.f64 1 (expm1.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))))
	31.0b	(+.f64 (/.f64 NdChar (+.f64 1 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))) (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))

Status

Error

Program

▶

0.0b

(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)))) (/.f64 NaChar (+.f64 1 (expm1.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))))

31.0b

(+.f64 (/.f64 NdChar (+.f64 1 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))) (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))

Compiler

Compiled 16957 to 5572 computations (67.1% saved)

localize59.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)
✓	0.0b	(expm1.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))))
	0.0b	(exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))
✓	0.5b	(log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))

series1.7s (10.2%)

Counts

2 → 120

Calls

2 calls:

1.6s	(log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))
68.0ms	(expm1.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))))

rewrite2.0ms (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:

1.0ms	(log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))
0.0ms	(expm1.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))))

simplify138.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

622×	`times-frac_binary64`
442×	`fma-def_binary64`
432×	`associate-/l*_binary64`
377×	`associate-/r*_binary64`
174×	`+-commutative_binary64`

Counts

142 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	520	6749
1	1743	6476
2	4974	6472
3	4998	6472

prune333.0ms (2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	290	1	291
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	291	2	293

Error

0.0b

Counts

293 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)))) (/.f64 NaChar (+.f64 1 (-.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))) 1))))
	31.0b	(+.f64 (/.f64 NdChar (+.f64 1 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))) (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))

Status

Error

Program

▶

0.0b

(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)))) (/.f64 NaChar (+.f64 1 (-.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))) 1))))

31.0b

(+.f64 (/.f64 NdChar (+.f64 1 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))) (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))

Compiler

Compiled 18128 to 6439 computations (64.5% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)
✓	0.0b	(exp.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))))
	0.0b	(exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))
	0.5b	(log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))

series1.6s (9.4%)

Counts

1 → 60

Calls

1 calls:

1.6s	(exp.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`exp-prod_binary64`
2×	`add-log-exp_binary64`
2×	`rem-exp-log_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`

Counts

1 → 14

Calls

1 calls:

1.0ms

(exp.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT))))

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

933×	`associate-/r*_binary64`
426×	`associate-/r/_binary64`
363×	`associate-+r+_binary64`
316×	`times-frac_binary64`
258×	`+-commutative_binary64`

Counts

74 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	3155
1	827	3050
2	3235	2799
3	5881	2799

prune478.0ms (2.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	295	1	296
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	296	2	298

Error

0.0b

Counts

298 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)))) (/.f64 NaChar (+.f64 1 (-.f64 (cbrt.f64 (pow.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT)))) 3)) 1))))
	31.0b	(+.f64 (/.f64 NdChar (+.f64 1 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))) (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))

Status

Error

Program

▶

0.0b

(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)))) (/.f64 NaChar (+.f64 1 (-.f64 (cbrt.f64 (pow.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT)))) 3)) 1))))

31.0b

(+.f64 (/.f64 NdChar (+.f64 1 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))) (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))

Compiler

Compiled 18525 to 6985 computations (62.3% saved)

localize121.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT))))
✓	0.0b	(exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT))
✓	0.3b	(cbrt.f64 (pow.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT)))) 3))
✓	0.5b	(log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT)))

series5.4s (32%)

Counts

4 → 240

Calls

4 calls:

2.0s	(exp.f64 (log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT))))
1.7s	(log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT)))
1.7s	(cbrt.f64 (pow.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT)))) 3))
61.0ms	(exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
25×	`exp-prod_binary64`
18×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`

Counts

4 → 81

Calls

4 calls:

11.0ms	(exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT))
2.0ms	(cbrt.f64 (pow.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT)))) 3))
1.0ms	(exp.f64 (log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT))))
0.0ms	(log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT)))

simplify196.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

629×	`times-frac_binary64`
507×	`fma-def_binary64`
442×	`associate-/l*_binary64`
386×	`associate-/r*_binary64`
233×	`+-commutative_binary64`

Counts

321 → 234

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	669	13765
1	2023	13223
2	5092	13223

prune324.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	234	2	236

Error

0.0b

Counts

236 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)))) (/.f64 NaChar (+.f64 1 (-.f64 (cbrt.f64 (pow.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT)))) 3)) 1))))
	31.0b	(+.f64 (/.f64 NdChar (+.f64 1 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))) (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))

Status

Error

Program

✓

0.0b

(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)))) (/.f64 NaChar (+.f64 1 (-.f64 (cbrt.f64 (pow.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 EAccept Ev) mu) Vef) KbT)))) 3)) 1))))

31.0b

(+.f64 (/.f64 NdChar (+.f64 1 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))) (sqrt.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (-.f64 (+.f64 (+.f64 Vef Ev) EAccept) mu) KbT)))))

Compiler

Compiled 16610 to 6610 computations (60.2% saved)

regimes2.2s (12.9%)

Accuracy

Total 0.0b remaining (55%)

Threshold costs 0.0b (55%)

Counts

150 → 1

Compiler

Compiled 60700 to 43728 computations (28% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`distribute-neg-in_binary64`
10×	`cancel-sign-sub-inv_binary64`
8×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	56
1	50	56
2	66	56
3	86	56
4	108	56
5	117	56
6	118	56
7	114	56

end101.0ms (0.6%)

Remove: (sort Ev EAccept)
Compiler: Compiled 275 to 193 computations (29.8% saved)

Details

analyze1.2s (7%)

sample2.0s (11.6%)

simplify94.0ms (0.6%)

prune5.0ms (0%)

localize23.0ms (0.1%)

series219.0ms (1.3%)

rewrite54.0ms (0.3%)

simplify187.0ms (1.1%)

prune375.0ms (2.2%)

localize59.0ms (0.3%)

series1.7s (10.2%)

rewrite2.0ms (0%)

simplify138.0ms (0.8%)

prune333.0ms (2%)

localize26.0ms (0.2%)

series1.6s (9.4%)

rewrite2.0ms (0%)

simplify77.0ms (0.5%)

prune478.0ms (2.8%)

localize121.0ms (0.7%)

series5.4s (32%)

rewrite19.0ms (0.1%)

simplify196.0ms (1.2%)

prune324.0ms (1.9%)

regimes2.2s (12.9%)

simplify7.0ms (0%)

end101.0ms (0.6%)

Profiling