Details

analyze43.0ms (1.3%)

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)

sample35.0ms (1%)

Algorithm

1×

intervals

Results

14.0ms	47×	body	2048	valid
8.0ms	61×	body	1024	valid
3.0ms	38×	body	512	valid
2.0ms	98×	body	128	valid
1.0ms	12×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify158.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4875	9
1	4875	9

prune5.0ms (0.2%)

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

29.8b

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))
4.4b	(-.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)
1.0ms	(exp.f64 (*.f64 a x))

series51.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

28.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
23.0ms	(exp.f64 (*.f64 a x))

simplify88.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4961	377
1	4961	377

prune37.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	5	35

Error

5.0b

Counts

35 → 5

Compiler

Compiled 412 to 207 computations (49.8% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
6.6b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
7.1b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
11.0b	(+.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)))))))

series262.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
87.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
46.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
41.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify43.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5442	1832

prune105.0ms (3.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Error

0.2b

Counts

91 → 6

Compiler

Compiled 2278 to 1349 computations (40.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
0.3b	(*.f64 x 1/6)
0.4b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
6.6b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite34.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
15×	`add-sqr-sqrt_binary64_1123`
11×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
10×	`-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136` `associate-r_binary64_1041` `associate-l*_binary64_1042`
8×	`associate-*r/_binary64_1043`
6×	`distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
4×	`*-commutative_binary64_1032` `add-log-exp_binary64_1140`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `unswap-sqr_binary64_1069`

Counts

4 → 90

Calls

4 calls:

10.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
8.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
6.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
4.0ms	(*.f64 x 1/6)

series199.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
77.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
34.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
11.0ms	(*.f64 x 1/6)

simplify49.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	6204	1933

prune102.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	102	6	108

Error

0.2b

Counts

108 → 6

Compiler

Compiled 2429 to 1406 computations (42.1% saved)

localize14.0ms (0.4%)

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)
0.4b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
7.8b	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

rewrite26.0ms (0.8%)

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))))
3.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))

series206.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
57.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))
33.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
10.0ms	(*.f64 x 1/6)

simplify75.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5086	1741

prune97.0ms (2.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	3	1	4
Picked	1	0	1
Done	1	0	1
Total	97	2	99

Error

0.0b

Counts

99 → 2

Compiler

Compiled 2245 to 1281 computations (42.9% saved)

regimes277.0ms (8.2%)

Accuracy

Total 0.4b remaining (89.5%)

Threshold costs 0.4b (89.5%)

Compiler

Compiled 2097 to 1546 computations (26.3% 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	41	85
1	41	85

end0.0ms (0%)

sample1.4s (41.3%)

Algorithm

1×

intervals

Results

407.0ms	1462×	body	2048	valid
238.0ms	1688×	body	1024	valid
91.0ms	1166×	body	512	valid
79.0ms	3063×	body	128	valid
31.0ms	621×	body	256	valid
3.0ms	104×	body	128	invalid

Compiler

Compiled 441 to 314 computations (28.8% saved)

Details

analyze43.0ms (1.3%)

sample35.0ms (1%)

simplify158.0ms (4.7%)

prune5.0ms (0.2%)

localize4.0ms (0.1%)

rewrite7.0ms (0.2%)

series51.0ms (1.5%)

simplify88.0ms (2.6%)

prune37.0ms (1.1%)

localize12.0ms (0.4%)

rewrite34.0ms (1%)

series262.0ms (7.8%)

simplify43.0ms (1.3%)

prune105.0ms (3.1%)

localize11.0ms (0.3%)

rewrite34.0ms (1%)

series199.0ms (5.9%)

simplify49.0ms (1.5%)

prune102.0ms (3%)

localize14.0ms (0.4%)

rewrite26.0ms (0.8%)

series206.0ms (6.1%)

simplify75.0ms (2.2%)

prune97.0ms (2.9%)

regimes277.0ms (8.2%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (41.3%)

Profiling