Details

analyze961.0ms (16.6%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample47.0ms (0.8%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
9.0ms	111×	body	128	invalid
7.0ms	78×	body	128	nan

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify199.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5019	19

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

1.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 k (+.f64 k 10))
0.0b	(*.f64 a (pow.f64 k m))
1.7b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64_1139`
17×	`add-sqr-sqrt_binary64_1123`
12×	`*-un-lft-identity_binary64_1101` `add-cbrt-cube_binary64_1137`
11×	`associate-r_binary64_1041`
10×	`add-cube-cbrt_binary64_1136`
7×	`prod-exp_binary64_1150`
6×	`associate-l_binary64_1042`
5×	`pow1_binary64_1162`
4×	`unpow-prod-down_binary64_1180` `div-exp_binary64_1152` `unswap-sqr_binary64_1069`
3×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `times-frac_binary64_1107` `associate-/r*_binary64_1045`
2×	`-commutative_binary64_1032` `pow-exp_binary64_1169` `flip3-+_binary64_1104` `associate-r/_binary64_1043` `associate-/r/_binary64_1047` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170`
1×	`distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `pow-prod-down_binary64_1172` `distribute-rgt-in_binary64_1051`

Counts

3 → 73

Calls

3 calls:

7.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
6.0ms	(*.f64 k (+.f64 k 10))
5.0ms	(*.f64 a (pow.f64 k m))

series207.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

122.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
60.0ms	(*.f64 a (pow.f64 k m))
25.0ms	(*.f64 k (+.f64 k 10))

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4956	1226
1	4956	1226

prune78.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Error

1.7b

Counts

83 → 5

Compiler

Compiled 1623 to 886 computations (45.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 k)
0.6b	(cbrt.f64 k)
0.6b	(cbrt.f64 k)
1.7b	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64_1139`
30×	`prod-exp_binary64_1150`
16×	`div-exp_binary64_1152`
13×	`add-cbrt-cube_binary64_1137`
11×	`pow-exp_binary64_1169`
9×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136` `cbrt-prod_binary64_1132`
8×	`pow-to-exp_binary64_1170`
4×	`add-log-exp_binary64_1140` `pow1_binary64_1162`
3×	`cbrt-unprod_binary64_1134` `pow1/3_binary64_1183` `times-frac_binary64_1107` `cbrt-undiv_binary64_1135` `associate-/r*_binary64_1045`
2×	`associate-/r/_binary64_1047`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `flip-+_binary64_1075`

Counts

4 → 71

Calls

4 calls:

11.0ms	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 1 (.f64 k (+.f64 k 10))))
1.0ms	(cbrt.f64 k)
1.0ms	(cbrt.f64 k)
1.0ms	(cbrt.f64 k)

series626.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

383.0ms	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 1 (.f64 k (+.f64 k 10))))
82.0ms	(cbrt.f64 k)
82.0ms	(cbrt.f64 k)
79.0ms	(cbrt.f64 k)

simplify51.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5391	1576

prune93.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	83	5	88

Error

1.7b

Counts

88 → 5

Compiler

Compiled 2163 to 1098 computations (49.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
0.1b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
12.6b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
12.6b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite79.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`add-sqr-sqrt_binary64_1123`
134×	`times-frac_binary64_1107`
76×	`*-un-lft-identity_binary64_1101` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
48×	`associate-r_binary64_1041`
45×	`unpow-prod-down_binary64_1180`
33×	`add-exp-log_binary64_1139`
24×	`associate-l_binary64_1042`
21×	`unswap-sqr_binary64_1069`
19×	`sqr-pow_binary64_1073`
18×	`add-cbrt-cube_binary64_1137`
13×	`div-exp_binary64_1152`
10×	`sqrt-div_binary64_1118`
8×	`prod-exp_binary64_1150` `pow1_binary64_1162`
7×	`associate-/l*_binary64_1046`
6×	`associate-/r/_binary64_1047` `associate-/r*_binary64_1045`
5×	`flip3-+_binary64_1104` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075`
4×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140`
3×	`pow-exp_binary64_1169` `div-inv_binary64_1098` `pow-to-exp_binary64_1170`
2×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`
1×	`-commutative_binary64_1032` `frac-times_binary64_1111` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `associate-*l/_binary64_1044`

Counts

4 → 218

Calls

4 calls:

37.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
8.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

series231.0ms (4%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
68.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
18.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
14.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify165.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4923	7913
1	4923	7913

prune453.0ms (7.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	230	5	235

Error

1.7b

Counts

235 → 5

Compiler

Compiled 8023 to 5256 computations (34.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 k (+.f64 k 10))
0.0b	(*.f64 a (pow.f64 k m))
0.2b	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
1.7b	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-exp-log_binary64_1139`
36×	`times-frac_binary64_1107`
34×	`add-sqr-sqrt_binary64_1123`
29×	`*-un-lft-identity_binary64_1101`
27×	`add-cube-cbrt_binary64_1136`
26×	`div-exp_binary64_1152`
22×	`add-cbrt-cube_binary64_1137`
16×	`prod-exp_binary64_1150`
11×	`associate-r_binary64_1041`
8×	`associate-/r*_binary64_1045`
7×	`pow1_binary64_1162` `cbrt-undiv_binary64_1135`
6×	`div-inv_binary64_1098` `associate-/l_binary64_1046` `associate-l*_binary64_1042`
5×	`pow-exp_binary64_1169` `1-exp_binary64_1145` `rec-exp_binary64_1151` `pow-to-exp_binary64_1170`
4×	`cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `add-log-exp_binary64_1140` `unswap-sqr_binary64_1069`
2×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip3-+_binary64_1104` `associate-/l/_binary64_1048` `associate-r/_binary64_1043` `flip-+_binary64_1075` `sqr-pow_binary64_1073`
1×	`inv-pow_binary64_1186` `distribute-lft-out_binary64_1052` `distribute-lft-in_binary64_1050` `associate-/r/_binary64_1047` `pow-prod-down_binary64_1172` `distribute-rgt-in_binary64_1051` `pow-flip_binary64_1175`

Counts

4 → 135

Calls

4 calls:

9.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
8.0ms	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))
6.0ms	(*.f64 k (+.f64 k 10))
5.0ms	(*.f64 a (pow.f64 k m))

series318.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))
114.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
56.0ms	(*.f64 a (pow.f64 k m))
29.0ms	(*.f64 k (+.f64 k 10))

simplify123.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4921	2954
1	4921	2954

prune143.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	148	4	152

Error

0.1b

Counts

152 → 4

Compiler

Compiled 3061 to 1791 computations (41.5% saved)

regimes176.0ms (3%)

Accuracy

Total 0.1b remaining (55.6%)

Threshold costs 0.1b (55.6%)

Compiler

Compiled 1588 to 1294 computations (18.5% saved)

bsearch29.0ms (0.5%)

Steps

Iters	Range		Point
8	3.861662612950994e-38	2.2239673020104246e-35	2.0291990054631206e-35

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	73
1	46	73

end0.0ms (0%)

sample1.6s (28%)

Algorithm

1×

intervals

Results

504.0ms	8000×	body	128	valid
276.0ms	3299×	body	128	invalid
87.0ms	1998×	body	128	nan

Compiler

Compiled 452 to 360 computations (20.4% saved)

Details

analyze961.0ms (16.6%)

sample47.0ms (0.8%)

simplify199.0ms (3.4%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite23.0ms (0.4%)

series207.0ms (3.6%)

simplify56.0ms (1%)

prune78.0ms (1.4%)

localize14.0ms (0.2%)

rewrite22.0ms (0.4%)

series626.0ms (10.8%)

simplify51.0ms (0.9%)

prune93.0ms (1.6%)

localize12.0ms (0.2%)

rewrite79.0ms (1.4%)

series231.0ms (4%)

simplify165.0ms (2.8%)

prune453.0ms (7.8%)

localize12.0ms (0.2%)

rewrite39.0ms (0.7%)

series318.0ms (5.5%)

simplify123.0ms (2.1%)

prune143.0ms (2.5%)

regimes176.0ms (3%)

bsearch29.0ms (0.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (28%)

Profiling