Details

analyze1.7s (8.8%)

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%)

Algorithm

1×

intervals

Results

113.0ms	127×	body	2048	valid
34.0ms	82×	body	1024	valid
10.0ms	18×	body	2048	overflowed
7.0ms	24×	body	1024	overflowed
7.0ms	330×	pre	128	true
7.0ms	28×	body	512	valid
3.0ms	14×	body	512	overflowed
1.0ms	7×	body	256	valid
1.0ms	7×	body	256	overflowed
1.0ms	12×	body	128	valid
1.0ms	11×	body	128	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify180.0ms (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: 61.3b

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 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.4b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.5b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
5.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite36.0ms (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:

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)

series276.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
84.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
46.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
45.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5130	1893

prune120.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 50.2b

Counts

94 → 3

Compiler

Compiled 3039 to 1288 computations (57.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.7b	(.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))))))
4.2b	(/.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)))))))
5.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
9.8b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite67.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 101

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))))
11.0ms	(.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))))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series8.8s (46%)

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)))))))
426.0ms	(.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))))
75.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4953	5349
1	4953	5349

prune271.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	113	3	116

Merged error: 0.0b

Counts

116 → 3

Compiler

Compiled 6209 to 3076 computations (50.5% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite17.0ms (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:

15.0ms

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

series20.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

20.0ms

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

simplify86.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5088	287

prune25.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	21	4	25

Merged error: 0.0b

Counts

25 → 4

Compiler

Compiled 360 to 275 computations (23.6% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
0.6b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.6b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.6b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

rewrite110.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`*-un-lft-identity_binary64_1088`
114×	`cbrt-prod_binary64_1116`
81×	`distribute-lft-out_binary64_1041`
60×	`div-inv_binary64_1085`
42×	`times-frac_binary64_1094`
37×	`add-sqr-sqrt_binary64_1109`
33×	`swap-sqr_binary64_1055` `cbrt-div_binary64_1117`
29×	`add-cube-cbrt_binary64_1120`
13×	`associate-r_binary64_1030` `associate-l_binary64_1031`
11×	`frac-add_binary64_1096` `flip-+_binary64_1062` `pow1_binary64_1146` `flip3-+_binary64_1091`
9×	`frac-times_binary64_1098` `pow1/3_binary64_1167`
6×	`add-exp-log_binary64_1123`
4×	`add-cbrt-cube_binary64_1121` `unswap-sqr_binary64_1056` `add-log-exp_binary64_1124`
3×	`associate-l/_binary64_1033` `associate-r/_binary64_1032`
2×	`pow-prod-down_binary64_1156` `pow-sqr_binary64_1061` `pow-prod-up_binary64_1155`
1×	`*-commutative_binary64_1021` `pow-plus_binary64_1148` `cbrt-unprod_binary64_1118` `pow2_binary64_1166` `prod-exp_binary64_1134`

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))))
15.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
15.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series639.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
162.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
151.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
146.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5290	4074

prune317.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Merged error: 0.0b

Counts

175 → 4

Compiler

Compiled 5429 to 4235 computations (22% saved)

regimes42.0ms (0.2%)

Compiler: Compiled 342 to 276 computations (19.3% 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%)

sample5.9s (31%)

Algorithm

1×

intervals

Results

3.4s	4094×	body	2048	valid
995.0ms	2412×	body	1024	valid
221.0ms	9806×	pre	128	true
209.0ms	398×	body	2048	overflowed
208.0ms	644×	body	1024	overflowed
173.0ms	708×	body	512	valid
68.0ms	320×	body	512	overflowed
44.0ms	262×	body	256	valid
36.0ms	514×	body	128	valid
22.0ms	161×	body	256	overflowed
20.0ms	282×	body	128	overflowed
14.0ms	10×	body	4096	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 157 to 127 computations (19.1% saved)

Details

analyze1.7s (8.8%)

sample199.0ms (1%)

simplify180.0ms (0.9%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite36.0ms (0.2%)

series276.0ms (1.5%)

simplify66.0ms (0.3%)

prune120.0ms (0.6%)

localize26.0ms (0.1%)

rewrite67.0ms (0.3%)

series8.8s (46%)

simplify99.0ms (0.5%)

prune271.0ms (1.4%)

localize5.0ms (0%)

rewrite17.0ms (0.1%)

series20.0ms (0.1%)

simplify86.0ms (0.4%)

prune25.0ms (0.1%)

localize9.0ms (0%)

rewrite110.0ms (0.6%)

series639.0ms (3.4%)

simplify68.0ms (0.4%)

prune317.0ms (1.7%)

regimes42.0ms (0.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.9s (31%)

Profiling