Details

analyze1.7s (8.7%)

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)

sample190.0ms (1%)

Algorithm

1×

intervals

Results

103.0ms	128×	body	2048	valid
31.0ms	73×	body	1024	valid
8.0ms	26×	body	1024	overflowed
7.0ms	315×	pre	128	true
7.0ms	12×	body	2048	overflowed
7.0ms	28×	body	512	valid
3.0ms	18×	body	128	valid
3.0ms	12×	body	512	overflowed
1.0ms	9×	body	256	valid
0.0ms	6×	body	128	overflowed
0.0ms	3×	body	256	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify173.0ms (0.9%)

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: 60.2b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.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)))
2.6b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.3b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786` `add-sqr-sqrt_binary64_772`
13×	`*-un-lft-identity_binary64_751`
10×	`add-log-exp_binary64_787` `flip--_binary64_726` `flip3--_binary64_755`
8×	`associate-/r/_binary64_699`
6×	`difference-of-squares_binary64_720`
4×	`prod-exp_binary64_797` `frac-times_binary64_761` `add-cube-cbrt_binary64_783` `pow1_binary64_809` `associate-*r/_binary64_695` `cbrt-undiv_binary64_782` `cbrt-unprod_binary64_781` `div-exp_binary64_799`
3×	`distribute-lft-out--_binary64_705` `diff-log_binary64_840` `difference-of-sqr-1_binary64_721` `sub-neg_binary64_744`
2×	`associate-/l/_binary64_700` `associate-*l/_binary64_696`
1×	`associate-/r_binary64_697` `times-frac_binary64_757` `div-inv_binary64_748` `frac-2neg_binary64_762` `clear-num_binary64_750` `associate-/l_binary64_698`

Counts

4 → 76

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 (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)

series637.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

472.0ms	(/.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)))
75.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
46.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
44.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify43.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5169	2234

prune132.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 0.0b

Counts

89 → 4

Compiler

Compiled 2950 to 1249 computations (57.7% 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_751`
7×	`distribute-lft-out_binary64_704`
6×	`times-frac_binary64_757`
4×	`div-inv_binary64_748`
3×	`add-cube-cbrt_binary64_783` `add-log-exp_binary64_787` `add-sqr-sqrt_binary64_772`
1×	`+-commutative_binary64_683` `flip3-+_binary64_754` `pow1_binary64_809` `add-cbrt-cube_binary64_784` `sum-log_binary64_839` `add-exp-log_binary64_786` `frac-add_binary64_759` `flip-+_binary64_725`

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))

simplify85.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5088	287

prune24.0ms (0.1%)

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

Merged error: 0.0b

Counts

26 → 5

Compiler

Compiled 439 to 320 computations (27.1% saved)

localize9.0ms (0%)

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))))

rewrite105.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`*-un-lft-identity_binary64_751`
114×	`cbrt-prod_binary64_779`
81×	`distribute-lft-out_binary64_704`
60×	`div-inv_binary64_748`
42×	`times-frac_binary64_757`
37×	`add-sqr-sqrt_binary64_772`
33×	`swap-sqr_binary64_718` `cbrt-div_binary64_780`
29×	`add-cube-cbrt_binary64_783`
13×	`associate-l_binary64_694` `associate-r_binary64_693`
11×	`flip3-+_binary64_754` `pow1_binary64_809` `frac-add_binary64_759` `flip-+_binary64_725`
9×	`pow1/3_binary64_830` `frac-times_binary64_761`
6×	`add-exp-log_binary64_786`
4×	`unswap-sqr_binary64_719` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784`
3×	`associate-r/_binary64_695` `associate-l/_binary64_696`
2×	`pow-sqr_binary64_724` `pow-prod-up_binary64_818` `pow-prod-down_binary64_819`
1×	`prod-exp_binary64_797` `pow-plus_binary64_811` `*-commutative_binary64_684` `cbrt-unprod_binary64_781` `pow2_binary64_829`

Counts

4 → 159

Calls

4 calls:

38.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series598.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
147.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
145.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
134.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5290	4074

prune333.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	171	5	176

Merged error: 0.0b

Counts

176 → 5

Compiler

Compiled 5587 to 4335 computations (22.4% saved)

localize27.0ms (0.1%)

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 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 (.f64 (pow.f64 eps 3) 1/6) b) (.f64 (*.f64 eps eps) 1/2))))))
4.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.1b	(.f64 (.f64 (pow.f64 eps 3) 1/6) b)
15.5b	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 (pow.f64 eps 3) 1/6) b) (.f64 (.f64 eps eps) 1/2)))

rewrite54.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_786`
26×	`add-cbrt-cube_binary64_784`
14×	`prod-exp_binary64_797`
11×	`pow1_binary64_809` `add-sqr-sqrt_binary64_772`
10×	`cbrt-unprod_binary64_781`
9×	`*-un-lft-identity_binary64_751`
8×	`associate-/r/_binary64_699`
6×	`add-cube-cbrt_binary64_783` `add-log-exp_binary64_787` `associate-r/_binary64_695` `associate-r*_binary64_693`
5×	`flip--_binary64_726` `flip3--_binary64_755`
4×	`frac-times_binary64_761` `flip3-+_binary64_754` `pow-prod-down_binary64_819` `cbrt-undiv_binary64_782` `flip-+_binary64_725` `div-exp_binary64_799`
2×	`associate-/l/_binary64_700` `-commutative_binary64_684` `associate-l_binary64_694` `associate-l/_binary64_696` `difference-of-squares_binary64_720`
1×	`distribute-lft-out--_binary64_705` `pow-to-exp_binary64_817` `unswap-sqr_binary64_719` `pow-exp_binary64_816` `distribute-lft-in_binary64_702` `associate-/r_binary64_697` `times-frac_binary64_757` `div-inv_binary64_748` `diff-log_binary64_840` `difference-of-sqr-1_binary64_721` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `associate-/l_binary64_698` `distribute-rgt-in_binary64_703`

Counts

4 → 88

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

series8.4s (44.3%)

Counts

4 → 12

Calls

4 calls:

8.2s	(/.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 (.f64 (pow.f64 eps 3) 1/6) b) (.f64 (*.f64 eps eps) 1/2))))))
184.0ms	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 (pow.f64 eps 3) 1/6) b) (.f64 (.f64 eps eps) 1/2)))
76.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
36.0ms	(.f64 (.f64 (pow.f64 eps 3) 1/6) b)

simplify83.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5062	3681

prune187.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	99	6	105

Merged error: 0.0b

Counts

105 → 6

Compiler

Compiled 5050 to 2454 computations (51.4% saved)

regimes71.0ms (0.4%)

Compiler: Compiled 816 to 558 computations (31.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample6.0s (31.6%)

Algorithm

1×

intervals

Results

3.4s	4066×	body	2048	valid
999.0ms	2371×	body	1024	valid
223.0ms	9744×	pre	128	true
208.0ms	629×	body	1024	overflowed
205.0ms	388×	body	2048	overflowed
196.0ms	761×	body	512	valid
65.0ms	286×	body	512	overflowed
44.0ms	278×	body	256	valid
37.0ms	514×	body	128	valid
21.0ms	153×	body	256	overflowed
21.0ms	288×	body	128	overflowed
14.0ms	10×	body	4096	valid

Compiler

Compiled 315 to 221 computations (29.8% saved)

Details

analyze1.7s (8.7%)

sample190.0ms (1%)

simplify173.0ms (0.9%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite39.0ms (0.2%)

series637.0ms (3.3%)

simplify43.0ms (0.2%)

prune132.0ms (0.7%)

localize5.0ms (0%)

rewrite15.0ms (0.1%)

series21.0ms (0.1%)

simplify85.0ms (0.4%)

prune24.0ms (0.1%)

localize9.0ms (0%)

rewrite105.0ms (0.6%)

series598.0ms (3.1%)

simplify69.0ms (0.4%)

prune333.0ms (1.7%)

localize27.0ms (0.1%)

rewrite54.0ms (0.3%)

series8.4s (44.3%)

simplify83.0ms (0.4%)

prune187.0ms (1%)

regimes71.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.0s (31.6%)

Profiling