Details

analyze1.8s (12.7%)

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 31 to 24 computations (22.6% saved)

sample210.0ms (1.5%)

Algorithm

1×

intervals

Results

144.0ms	161×	body	2048	valid
24.0ms	56×	body	1024	valid
7.0ms	312×	pre	128	true
5.0ms	18×	body	1024	overflowed
5.0ms	9×	body	2048	overflowed
4.0ms	17×	body	512	valid
2.0ms	11×	body	512	overflowed
1.0ms	17×	body	128	valid
1.0ms	8×	body	256	overflowed
1.0ms	1×	body	4096	valid
1.0ms	10×	body	128	overflowed
1.0ms	4×	body	256	valid

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify186.0ms (1.3%)

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

Merged error: 60.1b

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))
1.5b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
2.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.8b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1477`
26×	`*-un-lft-identity_binary64_1455`
15×	`cancel-sign-sub-inv_binary64_1421`
11×	`add-cube-cbrt_binary64_1490`
10×	`difference-of-squares_binary64_1424` `add-log-exp_binary64_1494`
9×	`flip--_binary64_1430` `flip3--_binary64_1459`
7×	`associate-r_binary64_1395` `associate-l_binary64_1396`
6×	`pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
5×	`distribute-lft-out--_binary64_1407` `sub-neg_binary64_1448` `difference-of-sqr-1_binary64_1425`
4×	`distribute-rgt-in_binary64_1405` `frac-times_binary64_1465` `distribute-lft-in_binary64_1404`
3×	`diff-log_binary64_1547`
2×	`associate-r/_binary64_1397` `associate-l/_binary64_1398`
1×	`prod-exp_binary64_1504` `*-commutative_binary64_1386` `cbrt-unprod_binary64_1488` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

4 → 96

Calls

4 calls:

13.0ms	(.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)
5.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series258.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
78.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
44.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
42.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4986	2058
1	4986	2058

prune182.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	3	109

Merged error: 52.5b

Counts

109 → 3

Compiler

Compiled 4265 to 2037 computations (52.2% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.3b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
5.8b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))
6.2b	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
9.1b	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_1493`
26×	`add-cbrt-cube_binary64_1491`
14×	`prod-exp_binary64_1504`
11×	`pow1_binary64_1516`
10×	`cbrt-unprod_binary64_1488`
8×	`associate-/r/_binary64_1401`
7×	`add-sqr-sqrt_binary64_1477`
6×	`associate-r/_binary64_1397` `add-log-exp_binary64_1494` `add-cube-cbrt_binary64_1490` `-un-lft-identity_binary64_1455`
5×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
4×	`associate-r_binary64_1395` `div-exp_binary64_1506` `frac-times_binary64_1465` `flip--_binary64_1430` `cbrt-undiv_binary64_1489` `flip3--_binary64_1459` `associate-l_binary64_1396` `pow-prod-down_binary64_1526`
2×	`associate-/l/_binary64_1402` `-commutative_binary64_1386` `associate-l/_binary64_1398`
1×	`distribute-rgt-in_binary64_1405` `clear-num_binary64_1454` `associate-/r_binary64_1399` `pow-to-exp_binary64_1524` `frac-2neg_binary64_1466` `associate-/l_binary64_1400` `distribute-lft-in_binary64_1404` `div-inv_binary64_1452` `pow-exp_binary64_1523` `sum-log_binary64_1546` `times-frac_binary64_1461` `+-commutative_binary64_1385` `unswap-sqr_binary64_1423`

Counts

4 → 84

Calls

4 calls:

18.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
13.0ms	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))
8.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))
7.0ms	(.f64 eps (.f64 1/6 (pow.f64 a 3)))

series3.7s (26.1%)

Counts

4 → 12

Calls

4 calls:

3.4s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
185.0ms	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))
78.0ms	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
73.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4975	3710
1	4975	3710

prune275.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	96	3	99

Merged error: 0.0b

Counts

99 → 3

Compiler

Compiled 6790 to 3673 computations (45.9% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1455`
7×	`distribute-lft-out_binary64_1406`
6×	`times-frac_binary64_1461`
4×	`div-inv_binary64_1452`
3×	`add-sqr-sqrt_binary64_1477` `add-log-exp_binary64_1494` `add-cube-cbrt_binary64_1490`
1×	`flip-+_binary64_1429` `pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `flip3-+_binary64_1458` `sum-log_binary64_1546` `+-commutative_binary64_1385` `frac-add_binary64_1463` `add-exp-log_binary64_1493`

Counts

1 → 19

Calls

1 calls:

18.0ms

(+.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))

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4970	287
1	4970	287

prune43.0ms (0.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	20	5	25

Merged error: 0.0b

Counts

25 → 5

Compiler

Compiled 705 to 569 computations (19.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

rewrite114.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`*-un-lft-identity_binary64_1455`
114×	`cbrt-prod_binary64_1486`
81×	`distribute-lft-out_binary64_1406`
60×	`div-inv_binary64_1452`
42×	`times-frac_binary64_1461`
37×	`add-sqr-sqrt_binary64_1477`
33×	`swap-sqr_binary64_1422` `cbrt-div_binary64_1487`
29×	`add-cube-cbrt_binary64_1490`
13×	`associate-r_binary64_1395` `associate-l_binary64_1396`
11×	`flip-+_binary64_1429` `pow1_binary64_1516` `flip3-+_binary64_1458` `frac-add_binary64_1463`
9×	`pow1/3_binary64_1537` `frac-times_binary64_1465`
6×	`add-exp-log_binary64_1493`
4×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `unswap-sqr_binary64_1423`
3×	`associate-r/_binary64_1397` `associate-l/_binary64_1398`
2×	`pow-prod-up_binary64_1525` `pow-prod-down_binary64_1526` `pow-sqr_binary64_1428`
1×	`prod-exp_binary64_1504` `pow-plus_binary64_1518` `*-commutative_binary64_1386` `pow2_binary64_1536` `cbrt-unprod_binary64_1488`

Counts

4 → 159

Calls

4 calls:

41.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
19.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
15.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
15.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series598.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
143.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
140.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
137.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4918	4109
1	4918	4109

prune355.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	170	6	176

Merged error: 0.0b

Counts

176 → 6

Compiler

Compiled 5723 to 4475 computations (21.8% saved)

regimes77.0ms (0.5%)

Compiler: Compiled 654 to 552 computations (15.6% saved)

bsearch1.0ms (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	133
1	51	133

end0.0ms (0%)

sample6.0s (41.7%)

Algorithm

1×

intervals

Results

3.4s	4066×	body	2048	valid
1.0s	2403×	body	1024	valid
214.0ms	9690×	pre	128	true
197.0ms	599×	body	1024	overflowed
187.0ms	734×	body	512	valid
186.0ms	354×	body	2048	overflowed
62.0ms	288×	body	512	overflowed
46.0ms	274×	body	256	valid
37.0ms	513×	body	128	valid
21.0ms	300×	body	128	overflowed
20.0ms	148×	body	256	overflowed
14.0ms	10×	body	4096	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 274 to 206 computations (24.8% saved)

Details

analyze1.8s (12.7%)

sample210.0ms (1.5%)

simplify186.0ms (1.3%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite39.0ms (0.3%)

series258.0ms (1.8%)

simplify76.0ms (0.5%)

prune182.0ms (1.3%)

localize26.0ms (0.2%)

rewrite59.0ms (0.4%)

series3.7s (26.1%)

simplify70.0ms (0.5%)

prune275.0ms (1.9%)

localize5.0ms (0%)

rewrite20.0ms (0.1%)

series21.0ms (0.1%)

simplify61.0ms (0.4%)

prune43.0ms (0.3%)

localize9.0ms (0.1%)

rewrite114.0ms (0.8%)

series598.0ms (4.2%)

simplify73.0ms (0.5%)

prune355.0ms (2.5%)

regimes77.0ms (0.5%)

bsearch1.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.0s (41.7%)

Profiling