Details

analyze1.7s (9.1%)

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)

sample199.0ms (1.1%)

Algorithm

1×

intervals

Results

111.0ms	130×	body	2048	valid
30.0ms	71×	body	1024	valid
8.0ms	15×	body	2048	overflowed
8.0ms	24×	body	1024	overflowed
7.0ms	324×	pre	128	true
7.0ms	9×	body	512	overflowed
6.0ms	25×	body	512	valid
2.0ms	22×	body	128	valid
1.0ms	1×	body	4096	valid
1.0ms	16×	body	128	overflowed
1.0ms	7×	body	256	valid
1.0ms	1×	body	2048	invalid
0.0ms	3×	body	256	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify177.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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

Merged error: 59.3b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.9b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.7b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
6.3b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1109`
21×	`*-un-lft-identity_binary64_1088`
10×	`add-log-exp_binary64_1124` `difference-of-squares_binary64_1057`
9×	`flip3--_binary64_1092` `flip--_binary64_1063`
7×	`associate-r_binary64_1030` `associate-l_binary64_1031`
6×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `pow1_binary64_1146` `add-cube-cbrt_binary64_1120`
5×	`difference-of-sqr-1_binary64_1058` `sub-neg_binary64_1081` `distribute-lft-out--_binary64_1042`
4×	`frac-times_binary64_1098`
3×	`diff-log_binary64_1177`
2×	`associate-l/_binary64_1033` `associate-r/_binary64_1032`
1×	`*-commutative_binary64_1021` `unswap-sqr_binary64_1056` `cbrt-unprod_binary64_1118` `distribute-rgt-in_binary64_1040` `pow-prod-down_binary64_1156` `prod-exp_binary64_1134` `distribute-lft-in_binary64_1039`

Counts

4 → 81

Calls

4 calls:

15.0ms	(.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)
5.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series249.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
74.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
42.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
41.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5130	1893

prune125.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 48.1b

Counts

94 → 4

Compiler

Compiled 3080 to 1316 computations (57.3% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b	(/.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)))))))
3.9b	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
6.3b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
15.2b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite57.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_1123`
26×	`add-cbrt-cube_binary64_1121`
14×	`prod-exp_binary64_1134`
11×	`add-sqr-sqrt_binary64_1109` `pow1_binary64_1146`
10×	`cbrt-unprod_binary64_1118`
9×	`*-un-lft-identity_binary64_1088`
8×	`associate-/r/_binary64_1036`
6×	`add-log-exp_binary64_1124` `add-cube-cbrt_binary64_1120` `associate-*r/_binary64_1032`
5×	`flip3--_binary64_1092` `flip--_binary64_1063`
4×	`associate-r_binary64_1030` `frac-times_binary64_1098` `div-exp_binary64_1136` `associate-l_binary64_1031` `flip-+_binary64_1062` `cbrt-undiv_binary64_1119` `pow-prod-down_binary64_1156` `flip3-+_binary64_1091`
2×	`-commutative_binary64_1021` `associate-l/_binary64_1033` `associate-/l/_binary64_1037` `difference-of-squares_binary64_1057`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `unswap-sqr_binary64_1056` `difference-of-sqr-1_binary64_1058` `distribute-rgt-in_binary64_1040` `associate-/r_binary64_1034` `sub-neg_binary64_1081` `times-frac_binary64_1094` `pow-exp_binary64_1153` `diff-log_binary64_1177` `pow-to-exp_binary64_1154` `distribute-lft-out--_binary64_1042` `associate-/l_binary64_1035` `distribute-lft-in_binary64_1039` `div-inv_binary64_1085`

Counts

4 → 88

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 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
13.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
7.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series8.4s (44.9%)

Counts

4 → 12

Calls

4 calls:

8.1s	(/.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)))))))
176.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
81.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
72.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))

simplify108.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4953	3679
1	4953	3679

prune222.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	100	4	104

Merged error: 0.1b

Counts

104 → 4

Compiler

Compiled 5179 to 2547 computations (50.8% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1088`
7×	`distribute-lft-out_binary64_1041`
6×	`times-frac_binary64_1094`
4×	`div-inv_binary64_1085`
3×	`add-sqr-sqrt_binary64_1109` `add-log-exp_binary64_1124` `add-cube-cbrt_binary64_1120`
1×	`frac-add_binary64_1096` `add-cbrt-cube_binary64_1121` `sum-log_binary64_1176` `add-exp-log_binary64_1123` `+-commutative_binary64_1020` `flip-+_binary64_1062` `pow1_binary64_1146` `flip3-+_binary64_1091`

Counts

1 → 19

Calls

1 calls:

14.0ms

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

series21.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5088	287

prune26.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	19	7	26

Merged error: 0.1b

Counts

26 → 7

Compiler

Compiled 410 to 312 computations (23.9% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

15.1b

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

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_1088`
6×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
4×	`times-frac_binary64_1094` `associate-/l*_binary64_1035`
3×	`add-sqr-sqrt_binary64_1109` `add-cube-cbrt_binary64_1120`
2×	`associate-/l/_binary64_1037` `div-exp_binary64_1136` `cbrt-undiv_binary64_1119` `distribute-lft-out_binary64_1041`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `cbrt-unprod_binary64_1118` `associate-/r*_binary64_1034` `flip-+_binary64_1062` `prod-exp_binary64_1134` `add-log-exp_binary64_1124` `pow1_binary64_1146` `flip3-+_binary64_1091` `div-inv_binary64_1085`

Counts

1 → 25

Calls

1 calls:

7.0ms

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

series64.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

64.0ms

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

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4975	354
1	4975	354

prune17.0ms (0.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	28	7	35

Merged error: 0.1b

Counts

35 → 7

Compiler

Compiled 316 to 94 computations (70.3% saved)

regimes316.0ms (1.7%)

Compiler: Compiled 4430 to 3124 computations (29.5% 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	51	137
1	51	137

end0.0ms (0%)

sample6.7s (35.7%)

Algorithm

1×

intervals

Results

3.5s	4073×	body	2048	valid
1.1s	2467×	body	1024	valid
228.0ms	9641×	pre	128	true
211.0ms	387×	body	2048	overflowed
192.0ms	708×	body	512	valid
185.0ms	548×	body	1024	overflowed
68.0ms	288×	body	512	overflowed
39.0ms	500×	body	128	valid
39.0ms	237×	body	256	valid
22.0ms	15×	body	4096	valid
21.0ms	143×	body	256	overflowed
20.0ms	273×	body	128	overflowed
2.0ms	2×	body	2048	invalid

Compiler

Compiled 1220 to 851 computations (30.2% saved)

Details

analyze1.7s (9.1%)

sample199.0ms (1.1%)

simplify177.0ms (0.9%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite38.0ms (0.2%)

series249.0ms (1.3%)

simplify67.0ms (0.4%)

prune125.0ms (0.7%)

localize26.0ms (0.1%)

rewrite57.0ms (0.3%)

series8.4s (44.9%)

simplify108.0ms (0.6%)

prune222.0ms (1.2%)

localize5.0ms (0%)

rewrite15.0ms (0.1%)

series21.0ms (0.1%)

simplify88.0ms (0.5%)

prune26.0ms (0.1%)

localize5.0ms (0%)

rewrite9.0ms (0%)

series64.0ms (0.3%)

simplify69.0ms (0.4%)

prune17.0ms (0.1%)

regimes316.0ms (1.7%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.7s (35.7%)

Profiling