Details

analyze1.6s (14.3%)

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)

sample173.0ms (1.6%)

Algorithm

1×

intervals

Results

92.0ms	120×	body	2048	valid
32.0ms	74×	body	1024	valid
8.0ms	38×	body	512	valid
7.0ms	317×	pre	128	true
7.0ms	25×	body	1024	overflowed
6.0ms	12×	body	2048	overflowed
1.0ms	17×	body	128	valid
1.0ms	7×	body	256	valid
1.0ms	14×	body	128	overflowed
1.0ms	6×	body	256	overflowed
1.0ms	4×	body	512	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify107.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5217	37

prune6.0ms (0.1%)

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

60.0b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize17.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(exp.f64 (*.f64 b eps))
0.0b	(*.f64 (+.f64 a b) eps)
0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(exp.f64 (*.f64 (+.f64 a b) eps))
0.3b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
3.1b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
6.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite35.0ms (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

8 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 a eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
0.0ms	(exp.f64 (*.f64 (+.f64 a b) eps))

series339.0ms (3.1%)

Counts

4 → 40

Calls

4 calls:

163.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
63.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
56.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
56.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

Compiler

Compiled 2065 to 1586 computations (23.2% saved)

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4964	2491
1	4964	2491

prune187.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	6	137

Error

47.5b

Counts

137 → 6

Compiler

Compiled 4157 to 1697 computations (59.2% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

2.8b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (*.f64 b eps)))
0.0b	(*.f64 (+.f64 a b) eps)
0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(exp.f64 (*.f64 (+.f64 a b) eps))
0.0b	(*.f64 (+.f64 a b) eps)
2.8b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (*.f64 b eps)))
3.1b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
6.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
18×	`add-sqr-sqrt_binary64_1123`
16×	`*-un-lft-identity_binary64_1101`
10×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
8×	`add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
6×	`pow1_binary64_1162` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067`
4×	`difference-of-squares_binary64_1070` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-l_binary64_1042` `associate-*l/_binary64_1044`
3×	`associate-r_binary64_1041`
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-*r/_binary64_1043` `associate-/r/_binary64_1047`
1×	`-commutative_binary64_1032` `distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `associate-/l_binary64_1046` `times-frac_binary64_1107` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `unswap-sqr_binary64_1069` `associate-/r*_binary64_1045`

Counts

4 → 86

Calls

8 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 eps)))
6.0ms	(*.f64 (+.f64 a b) eps)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
0.0ms	(exp.f64 (*.f64 (+.f64 a b) eps))

series498.0ms (4.5%)

Counts

4 → 49

Calls

4 calls:

269.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (*.f64 b eps)))
90.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
86.0ms	(*.f64 (+.f64 a b) eps)
52.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

Compiler

Compiled 2032 to 1484 computations (27% saved)

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5302	2350

prune181.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	137	4	141

Error

0.0b

Counts

141 → 4

Compiler

Compiled 3311 to 1303 computations (60.6% saved)

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

4.9b	(/.f64 (*.f64 b eps) a)
0.0b	(+.f64 (/.f64 1 a) (+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a)))))
0.0b	(+.f64 eps (/.f64 (*.f64 b eps) a))
0.0b	(+.f64 eps (/.f64 (*.f64 b eps) a))
0.0b	(+.f64 (/.f64 1 a) (+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a)))))
4.9b	(/.f64 (*.f64 b eps) a)

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1101` `add-log-exp_binary64_1140`
8×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
6×	`frac-add_binary64_1109`
5×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136`
4×	`sum-log_binary64_1192` `flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162` `times-frac_binary64_1107` `associate-/r*_binary64_1045`
2×	`associate-*r/_binary64_1043` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-+r+_binary64_1033` `associate-/l*_binary64_1046`

Counts

3 → 52

Calls

6 calls:

14.0ms	(+.f64 (/.f64 1 a) (+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a)))))
5.0ms	(+.f64 eps (/.f64 (*.f64 b eps) a))
4.0ms	(/.f64 (*.f64 b eps) a)
0.0ms	(+.f64 eps (/.f64 (*.f64 b eps) a))
0.0ms	(+.f64 (/.f64 1 a) (+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a)))))

series402.0ms (3.6%)

Counts

3 → 37

Calls

3 calls:

241.0ms	(+.f64 (/.f64 1 a) (+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a)))))
99.0ms	(/.f64 (*.f64 b eps) a)
62.0ms	(+.f64 eps (/.f64 (*.f64 b eps) a))

Compiler

Compiled 998 to 861 computations (13.7% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4979	1659
1	4979	1659

prune91.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	90	3	93

Error

Counts

93 → 3

Compiler

Compiled 1871 to 919 computations (50.9% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite15.0ms (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

2 calls:

13.0ms	(+.f64 (/.f64 1 a) (/.f64 1 b))
0.0ms	(+.f64 (/.f64 1 a) (/.f64 1 b))

series60.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

60.0ms

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

Compiler

Compiled 102 to 126 computations (-23.5% saved)

simplify85.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4871	341
1	4871	341

prune20.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	31	3	34

Error

Counts

34 → 3

Compiler

Compiled 294 to 224 computations (23.8% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	203	1084
1	203	1084

regimes205.0ms (1.9%)

Compiler: Compiled 2145 to 1674 computations (22% saved)

bsearch0.0ms (0%)

regimes64.0ms (0.6%)

Compiler: Compiled 54 to 102 computations (-88.9% saved)

bsearch244.0ms (2.2%)

Steps

Iters	Range	Point
9	1.9832980024657112e-151	2.3369905187336126e-144	8.071783117028655e-150
7	-8.021604462079984e-83	-1.606825943350709e-84	-1.6295744545273143e-84
10	-3.341236261320411e+213	-1.7826945697583038e+196	-6.771126179695667e+208

Iters

Range

Point

1.9832980024657112e-151

2.3369905187336126e-144

8.071783117028655e-150

-8.021604462079984e-83

-1.606825943350709e-84

-1.6295744545273143e-84

-3.341236261320411e+213

-1.7826945697583038e+196

-6.771126179695667e+208

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes114.0ms (1%)

Compiler: Compiled 33 to 84 computations (-154.5% saved)

bsearch223.0ms (2%)

Steps

Iters	Range		Point
6	3325398988593.578	21061600908891.617	5297192707102.497
5	0.12644922347090384	0.3135616842901756	0.30870757120660736
7	2.622829545459453e-63	7.100213414529623e-62	3.999304639266981e-62
8	-6.1022247793181475e-52	-1.591402068599831e-56	-3.1775888093945033e-52

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes29.0ms (0.3%)

Compiler: Compiled 24 to 69 computations (-187.5% saved)

bsearch0.0ms (0%)

regimes25.0ms (0.2%)

Accuracy

Total 3.3b remaining (96.5%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch4.0ms (0%)

Compiler: Compiled 75 to 65 computations (13.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	58	90
1	58	90

end0.0ms (0%)

sample6.0s (54.4%)

Algorithm

1×

intervals

Results

3.0s	4087×	body	2048	valid
923.0ms	2380×	body	1024	valid
226.0ms	9673×	pre	128	true
182.0ms	751×	body	512	valid
174.0ms	575×	body	1024	overflowed
171.0ms	362×	body	2048	overflowed
56.0ms	281×	body	512	overflowed
40.0ms	532×	body	128	valid
38.0ms	238×	body	256	valid
21.0ms	159×	body	256	overflowed
19.0ms	293×	body	128	overflowed
17.0ms	12×	body	4096	valid
2.0ms	3×	body	2048	invalid

Compiler

Compiled 813 to 647 computations (20.4% saved)

Pareto

0.49295389126620126

Details

analyze1.6s (14.3%)

sample173.0ms (1.6%)

simplify107.0ms (1%)

prune6.0ms (0.1%)

localize17.0ms (0.2%)

rewrite35.0ms (0.3%)

series339.0ms (3.1%)

simplify84.0ms (0.8%)

prune187.0ms (1.7%)

localize14.0ms (0.1%)

rewrite41.0ms (0.4%)

series498.0ms (4.5%)

simplify53.0ms (0.5%)

prune181.0ms (1.6%)

localize11.0ms (0.1%)

rewrite28.0ms (0.3%)

series402.0ms (3.6%)

simplify66.0ms (0.6%)

prune91.0ms (0.8%)

localize5.0ms (0%)

rewrite15.0ms (0.1%)

series60.0ms (0.5%)

simplify85.0ms (0.8%)

prune20.0ms (0.2%)

simplify17.0ms (0.1%)

regimes205.0ms (1.9%)

bsearch0.0ms (0%)

regimes64.0ms (0.6%)

bsearch244.0ms (2.2%)

regimes114.0ms (1%)

bsearch223.0ms (2%)

regimes29.0ms (0.3%)

bsearch0.0ms (0%)

regimes25.0ms (0.2%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.0s (54.4%)

Profiling