Details

analyze689.0ms (10.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4937	96
1	4937	96
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample43.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	41×	body	2048	valid
10.0ms	158×	body	128	valid
5.0ms	25×	body	1024	valid
4.0ms	13×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	26×	body	128	nan
1.0ms	10×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify281.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (276.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

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

36.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1464`
14×	`*-un-lft-identity_binary64_1442`
9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
8×	`add-log-exp_binary64_1481` `add-cube-cbrt_binary64_1477`
6×	`times-frac_binary64_1448` `associate-/l*_binary64_1387` `sqrt-prod_binary64_1458` `difference-of-squares_binary64_1411`
5×	`pow1_binary64_1503`
4×	`cancel-sign-sub-inv_binary64_1408` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`distribute-lft-out--_binary64_1394`
2×	`cbrt-undiv_binary64_1476` `associate-/l/_binary64_1389` `sub-neg_binary64_1435` `sqrt-div_binary64_1459` `diff-log_binary64_1534` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `associate-/r*_binary64_1386` `rem-sqrt-square_binary64_1455` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `div-sub_binary64_1447`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series267.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
62.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify90.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4893	1983
1	4893	1983

prune132.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	74	12	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	12	87

Error

6.7b

Counts

87 → 12

Compiler

Compiled 2251 to 1365 computations (39.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.2b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
11.7b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite46.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
22×	`times-frac_binary64_1448`
19×	`*-un-lft-identity_binary64_1442`
17×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
13×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
12×	`add-sqr-sqrt_binary64_1464`
11×	`associate-/l*_binary64_1387` `add-cube-cbrt_binary64_1477`
6×	`associate-/r/_binary64_1388` `add-log-exp_binary64_1481`
5×	`associate-/r*_binary64_1386` `pow1_binary64_1503`
4×	`div-inv_binary64_1439` `distribute-lft-out_binary64_1393`
3×	`sqrt-prod_binary64_1458` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`clear-num_binary64_1441` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `frac-2neg_binary64_1453`
1×	`sqrt-pow1_binary64_1460` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `sub-neg_binary64_1435` `diff-log_binary64_1534` `pow1/2_binary64_1522`

Counts

4 → 102

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
12.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series463.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
151.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
72.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
38.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4993	3154
1	4993	3154

prune158.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	115	11	126

Error

6.6b

Counts

126 → 11

Compiler

Compiled 3422 to 2125 computations (37.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/3 (.f64 1 (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))))
0.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64_1480`
18×	`add-cbrt-cube_binary64_1478`
15×	`prod-exp_binary64_1491`
10×	`pow1_binary64_1503`
8×	`cbrt-unprod_binary64_1475` `add-log-exp_binary64_1481` `*-un-lft-identity_binary64_1442`
7×	`add-sqr-sqrt_binary64_1464`
6×	`add-cube-cbrt_binary64_1477`
4×	`div-exp_binary64_1493`
3×	`1-exp_binary64_1486` `associate-l_binary64_1383` `pow-prod-down_binary64_1513` `sqrt-prod_binary64_1458`
2×	`associate-*r/_binary64_1384` `cbrt-undiv_binary64_1476` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417`
1×	`sqrt-pow1_binary64_1460` `associate-r_binary64_1382` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `sub-neg_binary64_1435` `+-commutative_binary64_1372` `*-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`

Counts

4 → 65

Calls

4 calls:

14.0ms	(.f64 1/3 (.f64 1 (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series337.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

179.0ms	(.f64 1/3 (.f64 1 (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))))
66.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
30.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4887	1593
1	4887	1593

prune97.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	76	12	88

Error

6.6b

Counts

88 → 12

Compiler

Compiled 2035 to 1307 computations (35.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/3 a)
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1464`
16×	`*-un-lft-identity_binary64_1442`
14×	`add-cube-cbrt_binary64_1477`
9×	`times-frac_binary64_1448`
8×	`add-log-exp_binary64_1481`
6×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
5×	`pow1_binary64_1503`
4×	`cancel-sign-sub-inv_binary64_1408` `sqrt-prod_binary64_1458`
3×	`associate-/r_binary64_1386` `associate-/l_binary64_1387` `flip3--_binary64_1446` `flip--_binary64_1417`
2×	`sub-neg_binary64_1435` `sqrt-div_binary64_1459` `diff-log_binary64_1534` `difference-of-squares_binary64_1411`
1×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `rem-sqrt-square_binary64_1455` `div-inv_binary64_1439` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522` `distribute-lft-out--_binary64_1394` `div-exp_binary64_1493`

Counts

4 → 71

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
3.0ms	(/.f64 1/3 a)

series165.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
58.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
16.0ms	(/.f64 1/3 a)

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5290	1310

prune83.0ms (1.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	82	13	95

Error

6.6b

Counts

95 → 13

Compiler

Compiled 1788 to 1059 computations (40.8% saved)

regimes1.1s (16.8%)

Accuracy

Total 1.5b remaining (20.1%)

Threshold costs 0b (0%)

Compiler

Compiled 6187 to 4776 computations (22.8% saved)

bsearch110.0ms (1.7%)

Steps

Iters	Range	Point
8	2.2638181669607407e+105	9.452720283575445e+108	4.677485094739758e+106
11	-3.1102668624910226e-210	-1.6490693973481557e-235	-1.3703763978612727e-221
7	-8.716062596680604e+48	-5.726717217066498e+46	-6.738042698067906e+47

Iters

Range

Point

2.2638181669607407e+105

9.452720283575445e+108

4.677485094739758e+106

-3.1102668624910226e-210

-1.6490693973481557e-235

-1.3703763978612727e-221

-8.716062596680604e+48

-5.726717217066498e+46

-6.738042698067906e+47

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	123	88
1	123	88

end0.0ms (0%)

sample2.1s (32.4%)

Algorithm

1×

intervals

Results

288.0ms	1158×	body	2048	valid
283.0ms	5205×	body	128	valid
136.0ms	704×	body	1024	valid
131.0ms	398×	body	4096	valid
55.0ms	369×	body	512	valid
34.0ms	684×	body	128	nan
23.0ms	406×	body	128	invalid
17.0ms	166×	body	256	valid

Compiler

Compiled 1174 to 898 computations (23.5% saved)

Details

analyze689.0ms (10.5%)

sample43.0ms (0.7%)

simplify281.0ms (4.3%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite33.0ms (0.5%)

series267.0ms (4.1%)

simplify90.0ms (1.4%)

prune132.0ms (2%)

localize13.0ms (0.2%)

rewrite46.0ms (0.7%)

series463.0ms (7.1%)

simplify79.0ms (1.2%)

prune158.0ms (2.4%)

localize13.0ms (0.2%)

rewrite34.0ms (0.5%)

series337.0ms (5.1%)

simplify76.0ms (1.2%)

prune97.0ms (1.5%)

localize11.0ms (0.2%)

rewrite26.0ms (0.4%)

series165.0ms (2.5%)

simplify73.0ms (1.1%)

prune83.0ms (1.3%)

regimes1.1s (16.8%)

bsearch110.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (32.4%)

Profiling