Details

analyze39.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 7 to 7 computations (0% saved)

sample38.0ms (1.1%)

Algorithm

1×

intervals

Results

17.0ms	54×	body	2048	valid
8.0ms	52×	body	1024	valid
3.0ms	35×	body	512	valid
2.0ms	93×	body	128	valid
1.0ms	22×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify154.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4875	9
1	4875	9

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

29.4b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
4.1b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_1123`
6×	`*-un-lft-identity_binary64_1101` `add-log-exp_binary64_1140`
3×	`add-cube-cbrt_binary64_1136` `cancel-sign-sub-inv_binary64_1067`
2×	`difference-of-squares_binary64_1070` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
1×	`diff-log_binary64_1193` `rem-exp-log_binary64_1141` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `exp-prod_binary64_1153` `flip3--_binary64_1105` `exp-to-pow_binary64_1163`

Counts

2 → 28

Calls

2 calls:

4.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(exp.f64 (*.f64 a x))

series38.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

24.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
13.0ms	(exp.f64 (*.f64 a x))

simplify88.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4961	377
1	4961	377

prune36.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	28	6	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	6	35

Error

5.6b

Counts

35 → 6

Compiler

Compiled 427 to 219 computations (48.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
5.2b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
7.9b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
10.3b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite34.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_1139`
13×	`add-sqr-sqrt_binary64_1123` `add-cbrt-cube_binary64_1137`
10×	`pow1_binary64_1162`
9×	`-un-lft-identity_binary64_1101` `prod-exp_binary64_1150` `add-cube-cbrt_binary64_1136` `associate-l*_binary64_1042`
7×	`associate-r_binary64_1041`
6×	`add-log-exp_binary64_1140`
5×	`cbrt-unprod_binary64_1134`
4×	`associate-*r/_binary64_1043`
3×	`*-commutative_binary64_1032` `flip3-+_binary64_1104` `pow-prod-down_binary64_1172` `flip-+_binary64_1075`
2×	`distribute-lft-in_binary64_1050` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051`
1×	`pow-exp_binary64_1169` `sum-log_binary64_1192` `+-commutative_binary64_1031` `pow-to-exp_binary64_1170`

Counts

4 → 74

Calls

4 calls:

10.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
7.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
6.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
5.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))

series248.0ms (7%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
82.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
43.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
39.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))

simplify44.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5442	1832

prune98.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Error

0.1b

Counts

92 → 4

Compiler

Compiled 2231 to 1320 computations (40.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
0.3b	(*.f64 x 1/6)
0.7b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
9.7b	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1123`
12×	`add-exp-log_binary64_1139` `pow1_binary64_1162`
11×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
9×	`log-prod_binary64_1187`
6×	`unpow-prod-down_binary64_1180` `associate-r_binary64_1041`
4×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `pow-pow_binary64_1173` `unpow-prod-up_binary64_1179` `pow-prod-down_binary64_1172` `associate-l_binary64_1042`
3×	`rem-log-exp_binary64_1142` `distribute-lft-in_binary64_1050` `exp-prod_binary64_1153` `distribute-rgt-in_binary64_1051`
2×	`-commutative_binary64_1032` `pow-exp_binary64_1169` `associate-r/_binary64_1043` `unswap-sqr_binary64_1069` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170`
1×	`flip3-+_binary64_1104` `pow-unpow_binary64_1178` `flip-+_binary64_1075` `log-pow_binary64_1190`

Counts

4 → 81

Calls

4 calls:

8.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
4.0ms	(*.f64 x 1/6)
4.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))
4.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))

series203.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
66.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))
32.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
10.0ms	(*.f64 x 1/6)

simplify80.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5086	1741

prune104.0ms (3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	93	4	97

Error

0.0b

Counts

97 → 4

Compiler

Compiled 2323 to 1339 computations (42.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(.f64 a (.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (.f64 x 1/2)))
0.8b	(.f64 a (.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (.f64 x 1/2)))
1.9b	(.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (*.f64 x 1/2))
1.9b	(.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (*.f64 x 1/2))

rewrite56.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
42×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
12×	`associate-*r/_binary64_1043`
8×	`associate-l_binary64_1042` `associate-*l/_binary64_1044`
6×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
4×	`-commutative_binary64_1032` `add-log-exp_binary64_1140` `flip3-+_binary64_1104` `associate-r*_binary64_1041` `flip-+_binary64_1075`

Counts

4 → 106

Calls

4 calls:

12.0ms	(.f64 a (.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (.f64 x 1/2)))
12.0ms	(.f64 a (.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (.f64 x 1/2)))
10.0ms	(.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (*.f64 x 1/2))
9.0ms	(.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (*.f64 x 1/2))

series211.0ms (6%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(.f64 a (.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (.f64 x 1/2)))
54.0ms	(.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (*.f64 x 1/2))
54.0ms	(.f64 a (.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (.f64 x 1/2)))
47.0ms	(.f64 (.f64 a (+.f64 1/2 (.f64 a (.f64 x 1/6)))) (*.f64 x 1/2))

simplify82.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5074	2588

prune200.0ms (5.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Error

0.0b

Counts

122 → 4

Compiler

Compiled 4656 to 3117 computations (33.1% saved)

regimes284.0ms (8.1%)

Accuracy

Total 0.7b remaining (95%)

Threshold costs 0.7b (95%)

Compiler

Compiled 1703 to 1289 computations (24.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	74
1	45	74

end0.0ms (0%)

sample1.4s (39.8%)

Algorithm

1×

intervals

Results

420.0ms	1446×	body	2048	valid
256.0ms	1760×	body	1024	valid
94.0ms	1116×	body	512	valid
79.0ms	3076×	body	128	valid
35.0ms	602×	body	256	valid
4.0ms	134×	body	128	invalid

Compiler

Compiled 366 to 269 computations (26.5% saved)

Details

analyze39.0ms (1.1%)

sample38.0ms (1.1%)

simplify154.0ms (4.4%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite7.0ms (0.2%)

series38.0ms (1.1%)

simplify88.0ms (2.5%)

prune36.0ms (1%)

localize12.0ms (0.3%)

rewrite34.0ms (1%)

series248.0ms (7%)

simplify44.0ms (1.3%)

prune98.0ms (2.8%)

localize12.0ms (0.3%)

rewrite25.0ms (0.7%)

series203.0ms (5.8%)

simplify80.0ms (2.3%)

prune104.0ms (3%)

localize14.0ms (0.4%)

rewrite56.0ms (1.6%)

series211.0ms (6%)

simplify82.0ms (2.3%)

prune200.0ms (5.7%)

regimes284.0ms (8.1%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (39.8%)

Profiling