Details

analyze1.6s (12%)

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 31 to 24 computations (22.6% saved)

sample177.0ms (1.3%)

Algorithm

1×

intervals

Results

95.0ms	124×	body	2048	valid
38.0ms	89×	body	1024	valid
7.0ms	310×	pre	128	true
6.0ms	14×	body	2048	overflowed
6.0ms	20×	body	1024	overflowed
5.0ms	22×	body	512	valid
2.0ms	8×	body	512	overflowed
1.0ms	1×	body	4096	valid
1.0ms	14×	body	128	valid
1.0ms	6×	body	256	valid
1.0ms	10×	body	128	overflowed
0.0ms	2×	body	256	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify106.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	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

60.8b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
3.3b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.4b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1123`
26×	`*-un-lft-identity_binary64_1101`
15×	`cancel-sign-sub-inv_binary64_1067`
11×	`add-cube-cbrt_binary64_1136`
10×	`difference-of-squares_binary64_1070` `add-log-exp_binary64_1140`
9×	`flip--_binary64_1076` `flip3--_binary64_1105`
7×	`associate-r_binary64_1041` `associate-l_binary64_1042`
6×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
5×	`sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053`
4×	`frac-times_binary64_1111` `distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
3×	`diff-log_binary64_1193`
2×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069`

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

series145.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
45.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
28.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
23.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4967	2058
1	4967	2058

prune128.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	3	109

Error

49.8b

Counts

109 → 3

Compiler

Compiled 3415 to 1405 computations (58.9% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.3b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.5b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
5.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
14.1b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
16×	`add-sqr-sqrt_binary64_1123`
13×	`*-un-lft-identity_binary64_1101`
9×	`pow1_binary64_1162`
8×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
7×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `add-cube-cbrt_binary64_1136`
6×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-*r/_binary64_1043` `cancel-sign-sub-inv_binary64_1067`
4×	`difference-of-squares_binary64_1070` `frac-times_binary64_1111` `flip3-+_binary64_1104` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075`
3×	`associate-r_binary64_1041` `pow-prod-down_binary64_1172`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `associate-/l/_binary64_1048` `associate-*l/_binary64_1044`
1×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l_binary64_1046` `times-frac_binary64_1107` `associate-l_binary64_1042` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051` `associate-/r*_binary64_1045`

Counts

4 → 90

Calls

4 calls:

16.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
12.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series4.5s (32.8%)

Counts

4 → 12

Calls

4 calls:

4.3s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
97.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
43.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
27.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5131	3717

prune214.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	101	4	105

Error

0.0b

Counts

105 → 4

Compiler

Compiled 5348 to 2619 computations (51% saved)

localize7.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1101`
7×	`distribute-lft-out_binary64_1052`
6×	`times-frac_binary64_1107`
4×	`div-inv_binary64_1098`
3×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
1×	`sum-log_binary64_1192` `add-exp-log_binary64_1139` `pow1_binary64_1162` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `+-commutative_binary64_1031` `flip-+_binary64_1075` `frac-add_binary64_1109`

Counts

1 → 19

Calls

1 calls:

13.0ms

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

series10.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

9.0ms

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

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4871	287
1	4871	287

prune23.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	21	5	26

Error

Counts

26 → 5

Compiler

Compiled 432 to 317 computations (26.6% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

15.3b

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_1101`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
4×	`associate-/l*_binary64_1046` `times-frac_binary64_1107`
3×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136`
2×	`distribute-lft-out_binary64_1052` `associate-/l/_binary64_1048` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `pow1_binary64_1162` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `flip-+_binary64_1075` `associate-/r*_binary64_1045`

Counts

1 → 25

Calls

1 calls:

6.0ms

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

series30.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

30.0ms

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

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5070	354

prune15.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	28	5	33

Error

Counts

33 → 5

Compiler

Compiled 316 to 94 computations (70.3% saved)

regimes276.0ms (2%)

Accuracy

Total 0.3b remaining (80.7%)

Threshold costs 0.3b (80.7%)

Compiler

Compiled 4410 to 3000 computations (32% saved)

bsearch3.0ms (0%)

Compiler: Compiled 24 to 19 computations (20.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	137
1	49	137

end0.0ms (0%)

sample5.9s (43.5%)

Algorithm

1×

intervals

Results

3.0s	4065×	body	2048	valid
912.0ms	2393×	body	1024	valid
211.0ms	9614×	pre	128	true
181.0ms	781×	body	512	valid
170.0ms	566×	body	1024	overflowed
162.0ms	347×	body	2048	overflowed
64.0ms	301×	body	512	overflowed
36.0ms	524×	body	128	valid
31.0ms	223×	body	256	valid
23.0ms	14×	body	4096	valid
18.0ms	262×	body	128	overflowed
18.0ms	136×	body	256	overflowed
1.0ms	2×	body	2048	invalid

Compiler

Compiled 1215 to 820 computations (32.5% saved)

Details

analyze1.6s (12%)

sample177.0ms (1.3%)

simplify106.0ms (0.8%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite34.0ms (0.3%)

series145.0ms (1.1%)

simplify90.0ms (0.7%)

prune128.0ms (0.9%)

localize29.0ms (0.2%)

rewrite49.0ms (0.4%)

series4.5s (32.8%)

simplify69.0ms (0.5%)

prune214.0ms (1.6%)

localize7.0ms (0%)

rewrite14.0ms (0.1%)

series10.0ms (0.1%)

simplify80.0ms (0.6%)

prune23.0ms (0.2%)

localize4.0ms (0%)

rewrite10.0ms (0.1%)

series30.0ms (0.2%)

simplify55.0ms (0.4%)

prune15.0ms (0.1%)

regimes276.0ms (2%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (43.5%)

Profiling