Details

analyze2.0s (18.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample167.0ms (1.6%)

Algorithm

1×

intervals

Results

77.0ms	110×	body	2048	valid
32.0ms	87×	body	1024	valid
10.0ms	29×	body	512	valid
6.0ms	312×	pre	128	true
6.0ms	19×	body	1024	overflowed
4.0ms	9×	body	2048	overflowed
2.0ms	10×	body	512	overflowed
1.0ms	21×	body	128	valid
1.0ms	9×	body	256	valid
1.0ms	13×	body	128	overflowed
1.0ms	5×	body	256	overflowed

Compiler

Compiled 64 to 46 computations (28.1% saved)

simplify23.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

986×	`times-frac_binary64`
580×	`associate-/l*_binary64`
286×	`associate-/r*_binary64`
126×	`distribute-rgt-in_binary64`
122×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	44	37
2	105	37
3	238	37
4	834	37
5	5217	37

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

59.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	59.4b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))

Compiler

Compiled 81 to 57 computations (29.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
3.5b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.5b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
6.3b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite145.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

59.4b

Rules

33×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
15×	`cancel-sign-sub-inv_binary64`
11×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64`

Counts

4 → 96

Calls

4 calls:

12.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
5.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

Compiler

Compiled 2979 to 1270 computations (57.4% saved)

series161.0ms (1.5%)

Error

41.5b

Counts

4 → 44

Calls

4 calls:

56.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
25.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
24.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
22.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

Compiler

Compiled 3141 to 2071 computations (34.1% saved)

simplify117.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

525×	`distribute-rgt-in_binary64`
496×	`distribute-lft-in_binary64`
253×	`associate-+r+_binary64`
244×	`associate-+l+_binary64`
208×	`associate-r_binary64`

Counts

140 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	3007
1	470	2808
2	1654	2713
3	4839	2713
4	4993	2713

prune127.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	5	124

Error

41.4b

Counts

124 → 5

Alt Table

Status	Error	Program
▶	51.3b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (.f64 b (+.f64 eps (.f64 (.f64 1/2 (.f64 eps eps)) b)))))
	60.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 eps a)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
	54.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 (.f64 1/2 (.f64 a a)) eps))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
	60.5b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 a (.f64 eps (*.f64 eps b))))
	55.0b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps a) (-.f64 (exp.f64 (*.f64 b eps)) 1)))

Compiler

Compiled 2693 to 1216 computations (54.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.6b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (.f64 b (+.f64 eps (.f64 (.f64 1/2 (.f64 eps eps)) b)))))
4.5b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
6.3b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
9.2b	(.f64 (.f64 1/2 (*.f64 eps eps)) b)

rewrite208.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

41.3b

Rules

34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`prod-exp_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64`
13×	`pow1_binary64` `*-un-lft-identity_binary64`
10×	`associate-*r/_binary64`
8×	`add-log-exp_binary64` `associate-/r/_binary64`

Counts

4 → 92

Calls

4 calls:

17.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (.f64 b (+.f64 eps (.f64 (.f64 1/2 (.f64 eps eps)) b)))))
7.0ms	(.f64 (.f64 1/2 (*.f64 eps eps)) b)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

Compiler

Compiled 3769 to 1663 computations (55.9% saved)

series493.0ms (4.7%)

Error

1.4b

Counts

4 → 45

Calls

4 calls:

342.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (.f64 b (+.f64 eps (.f64 (.f64 1/2 (.f64 eps eps)) b)))))
47.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
24.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
21.0ms	(.f64 (.f64 1/2 (*.f64 eps eps)) b)

Compiler

Compiled 7108 to 4558 computations (35.9% saved)

simplify134.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

539×	`times-frac_binary64`
518×	`associate-l_binary64`
325×	`associate-/l*_binary64`
323×	`associate-/r*_binary64`
135×	`*-commutative_binary64`

Counts

137 → 124

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	408	5425
1	1238	4753
2	4914	4753
3	4980	4753

prune114.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	122	7	129

Error

1.4b

Counts

129 → 7

Alt Table

Status	Error	Program
▶	13.1b	(/.f64 (+.f64 b a) (*.f64 b a))
	51.3b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 eps a)) 1) (.f64 b (+.f64 eps (.f64 (.f64 1/2 (.f64 eps eps)) b)))))
	60.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 eps a)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
	53.7b	(/.f64 (.f64 eps (+.f64 (.f64 1/2 (.f64 (exp.f64 (.f64 eps a)) (.f64 (.f64 eps eps) (.f64 b b)))) (+.f64 (.f64 (exp.f64 (.f64 eps a)) (+.f64 (.f64 eps b) 1)) -1))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (.f64 b (+.f64 eps (.f64 (.f64 1/2 (.f64 eps eps)) b)))))
	54.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 (.f64 1/2 (.f64 a a)) eps))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
	55.0b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps a) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
	21.1b	(+.f64 (/.f64 1 a) (+.f64 (/.f64 1 b) (+.f64 (.f64 1/12 (.f64 eps (.f64 eps a))) (+.f64 (.f64 (.f64 (.f64 eps eps) b) 1/4) (.f64 1/6 (/.f64 (.f64 (.f64 eps eps) (.f64 b b)) a))))))

Compiler

Compiled 4202 to 1984 computations (52.8% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

13.5b

(/.f64 (+.f64 b a) (*.f64 b a))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`times-frac_binary64` `associate-/l*_binary64`
3×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
2×	`div-exp_binary64` `cbrt-undiv_binary64` `distribute-lft-out_binary64` `associate-/l/_binary64`

Counts

1 → 25

Calls

1 calls:

6.0ms

(/.f64 (+.f64 b a) (*.f64 b a))

Compiler

Compiled 318 to 85 computations (73.3% saved)

series29.0ms (0.3%)

Error

0.1b

Counts

1 → 12

Calls

1 calls:

24.0ms

(/.f64 (+.f64 b a) (*.f64 b a))

Compiler

Compiled 179 to 143 computations (20.1% saved)

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
441×	`associate-/r/_binary64`
349×	`distribute-rgt-in_binary64`
312×	`associate-l_binary64`
311×	`distribute-lft-in_binary64`

Counts

37 → 14

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	471
1	148	408
2	457	408
3	1454	408
4	3152	408
5	3535	408
6	5065	408

prune14.0ms (0.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	15	6	21

Error

0.1b

Counts

21 → 6

Alt Table

Status	Error	Program
✓	13.1b	(/.f64 (+.f64 b a) (*.f64 b a))
	51.3b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 eps a)) 1) (.f64 b (+.f64 eps (.f64 (.f64 1/2 (.f64 eps eps)) b)))))
	60.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 eps a)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
▶	4.4b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	53.7b	(/.f64 (.f64 eps (+.f64 (.f64 1/2 (.f64 (exp.f64 (.f64 eps a)) (.f64 (.f64 eps eps) (.f64 b b)))) (+.f64 (.f64 (exp.f64 (.f64 eps a)) (+.f64 (.f64 eps b) 1)) -1))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (.f64 b (+.f64 eps (.f64 (.f64 1/2 (.f64 eps eps)) b)))))
	54.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 (.f64 1/2 (.f64 a a)) eps))) (-.f64 (exp.f64 (.f64 b eps)) 1)))

Compiler

Compiled 400 to 242 computations (39.5% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`*-un-lft-identity_binary64`
7×	`distribute-lft-out_binary64`
6×	`times-frac_binary64`
4×	`div-inv_binary64`
3×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`

Counts

1 → 19

Calls

1 calls:

12.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 234 to 182 computations (22.2% saved)

series19.0ms (0.2%)

Error

0.1b

Counts

1 → 12

Calls

1 calls:

17.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 179 to 143 computations (20.1% saved)

simplify80.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

664×	`div-sub_binary64`
610×	`unswap-sqr_binary64`
305×	`sub-neg_binary64`
281×	`distribute-rgt-in_binary64`
272×	`distribute-rgt-out_binary64`

Counts

31 → 10

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	370
1	100	340
2	220	337
3	472	337
4	990	337
5	2447	337
6	3565	337
7	4982	337

prune15.0ms (0.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	9	1	10
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	9	7	16

Error

0.1b

Counts

16 → 7

Alt Table

Status	Error	Program
	13.1b	(/.f64 (+.f64 b a) (*.f64 b a))
	51.3b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 eps a)) 1) (.f64 b (+.f64 eps (.f64 (.f64 1/2 (.f64 eps eps)) b)))))
	60.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 eps a)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
	4.4b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	53.7b	(/.f64 (.f64 eps (+.f64 (.f64 1/2 (.f64 (exp.f64 (.f64 eps a)) (.f64 (.f64 eps eps) (.f64 b b)))) (+.f64 (.f64 (exp.f64 (.f64 eps a)) (+.f64 (.f64 eps b) 1)) -1))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (.f64 b (+.f64 eps (.f64 (.f64 1/2 (.f64 eps eps)) b)))))
	54.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 (.f64 1/2 (.f64 a a)) eps))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
	30.1b	(/.f64 (-.f64 (/.f64 (/.f64 1 b) b) (/.f64 (/.f64 1 a) a)) (-.f64 (/.f64 1 b) (/.f64 1 a)))

Compiler

Compiled 291 to 202 computations (30.6% saved)

regimes955.0ms (9.1%)

Accuracy

Total 0.2b remaining (60.1%)

Threshold costs 0.2b (60.1%)

Compiler

Compiled 14878 to 9692 computations (34.9% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 27 to 19 computations (29.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`sub-neg_binary64` `+-commutative_binary64`
1×	`if-if-or-not_binary64` `1-exp_binary64` `*-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	133
1	47	133
2	50	133
3	48	133

end11.0ms (0.1%)

Remove: (sort a b)
Compiler: Compiled 267 to 147 computations (44.9% saved)

sample5.5s (52.7%)

Algorithm

1×

intervals

Results

3.0s	4172×	body	2048	valid
867.0ms	2302×	body	1024	valid
214.0ms	9694×	pre	128	true
188.0ms	389×	body	2048	overflowed
176.0ms	578×	body	1024	overflowed
156.0ms	703×	body	512	valid
58.0ms	301×	body	512	overflowed
40.0ms	571×	body	128	valid
34.0ms	242×	body	256	valid
19.0ms	297×	body	128	overflowed
19.0ms	129×	body	256	overflowed
12.0ms	10×	body	4096	valid

Compiler

Compiled 308 to 196 computations (36.4% saved)

Details

analyze2.0s (18.7%)

sample167.0ms (1.6%)

simplify23.0ms (0.2%)

prune3.0ms (0%)

localize16.0ms (0.2%)

rewrite145.0ms (1.4%)

series161.0ms (1.5%)

simplify117.0ms (1.1%)

prune127.0ms (1.2%)

localize18.0ms (0.2%)

rewrite208.0ms (2%)

series493.0ms (4.7%)

simplify134.0ms (1.3%)

prune114.0ms (1.1%)

localize4.0ms (0%)

rewrite28.0ms (0.3%)

series29.0ms (0.3%)

simplify69.0ms (0.7%)

prune14.0ms (0.1%)

localize5.0ms (0%)

rewrite30.0ms (0.3%)

series19.0ms (0.2%)

simplify80.0ms (0.8%)

prune15.0ms (0.1%)

regimes955.0ms (9.1%)

bsearch6.0ms (0.1%)

simplify5.0ms (0%)

end11.0ms (0.1%)

sample5.5s (52.7%)

Profiling