Details

analyze260.0ms (7.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample53.0ms (1.6%)

Algorithm

1×

intervals

Results

21.0ms	131×	body	2048	nan
11.0ms	256×	body	128	valid
6.0ms	52×	body	1024	nan
4.0ms	35×	body	512	nan
1.0ms	16×	body	256	nan
1.0ms	18×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify244.0ms (7.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14

prune3.0ms (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 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.0b	(-.f64 (*.f64 x x) 1)
27.4b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1101`
9×	`add-sqr-sqrt_binary64_1123`
6×	`sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
5×	`add-log-exp_binary64_1140` `pow1_binary64_1162`
4×	`difference-of-squares_binary64_1070` `add-exp-log_binary64_1139` `log-prod_binary64_1187`
3×	`add-cbrt-cube_binary64_1137` `cancel-sign-sub-inv_binary64_1067`
2×	`difference-of-sqr-1_binary64_1071` `flip--_binary64_1076` `flip3--_binary64_1105` `sqrt-div_binary64_1118` `log-div_binary64_1188`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `distribute-lft-out_binary64_1052` `sub-neg_binary64_1094` `rem-log-exp_binary64_1142` `sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `flip-+_binary64_1075` `log-pow_binary64_1190` `pow1/2_binary64_1181`

Counts

3 → 50

Calls

3 calls:

8.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
5.0ms	(-.f64 (*.f64 x x) 1)

series102.0ms (3%)

Counts

3 → 16

Calls

3 calls:

40.0ms	(-.f64 (*.f64 x x) 1)
31.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
30.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 231 to 205 computations (11.3% saved)

simplify59.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5082	785

prune56.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	2	67

Error

Counts

67 → 2

Compiler

Compiled 852 to 549 computations (35.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.0b	(sqrt.f64 (-.f64 x 1))
0.4b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_1123`
26×	`sqrt-prod_binary64_1117`
21×	`*-un-lft-identity_binary64_1101`
16×	`sqrt-div_binary64_1118`
11×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
10×	`associate-r_binary64_1041`
7×	`add-exp-log_binary64_1139` `associate-l_binary64_1042`
6×	`add-cbrt-cube_binary64_1137`
5×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
4×	`difference-of-squares_binary64_1070` `frac-times_binary64_1111` `add-log-exp_binary64_1140` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `unswap-sqr_binary64_1069` `pow1/2_binary64_1181`
3×	`log-prod_binary64_1187` `pow-prod-down_binary64_1172`
2×	`rem-sqrt-square_binary64_1114` `distribute-lft-out_binary64_1052` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `associate-r/_binary64_1043` `log-div_binary64_1188` `associate-l/_binary64_1044`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `rem-log-exp_binary64_1142` `log-pow_binary64_1190` `sqrt-unprod_binary64_1121`

Counts

4 → 92

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
4.0ms	(sqrt.f64 (-.f64 x 1))
3.0ms	(sqrt.f64 (+.f64 x 1))
3.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))

series90.0ms (2.7%)

Counts

4 → 16

Calls

4 calls:

37.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
24.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
14.0ms	(sqrt.f64 (+.f64 x 1))
13.0ms	(sqrt.f64 (-.f64 x 1))

Compiler

Compiled 322 to 275 computations (14.6% saved)

simplify81.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5115	1619

prune105.0ms (3.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	108	2	110

Error

Counts

110 → 2

Compiler

Compiled 1855 to 1409 computations (24% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
0.0b	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
27.4b	(sqrt.f64 (-.f64 (*.f64 x x) 1))
27.4b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite34.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`sqrt-prod_binary64_1117`
16×	`*-un-lft-identity_binary64_1101`
14×	`add-sqr-sqrt_binary64_1123` `log-prod_binary64_1187`
10×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
8×	`sqrt-div_binary64_1118`
6×	`add-exp-log_binary64_1139` `log-pow_binary64_1190`
4×	`difference-of-squares_binary64_1070` `add-log-exp_binary64_1140` `sqrt-pow1_binary64_1119` `add-cbrt-cube_binary64_1137` `log-div_binary64_1188` `pow1/2_binary64_1181`
2×	`rem-sqrt-square_binary64_1114` `distribute-lft-out_binary64_1052` `rem-log-exp_binary64_1142` `difference-of-sqr-1_binary64_1071` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `flip-+_binary64_1075`

Counts

4 → 76

Calls

4 calls:

9.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
8.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series124.0ms (3.7%)

Counts

4 → 20

Calls

4 calls:

40.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
37.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
24.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
22.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))

Compiler

Compiled 652 to 526 computations (19.3% saved)

simplify93.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4906	1526
1	4906	1526

prune118.0ms (3.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	96	2	98

Error

Counts

98 → 2

Compiler

Compiled 2434 to 1593 computations (34.6% saved)

regimes67.0ms (2%)

Accuracy

Total 0.0b remaining (4.9%)

Threshold costs 0.0b (4.9%)

Compiler

Compiled 423 to 324 computations (23.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample1.8s (53.2%)

Algorithm

1×

intervals

Results

657.0ms	4027×	body	2048	nan
337.0ms	8000×	body	128	valid
248.0ms	1996×	body	1024	nan
100.0ms	1067×	body	512	nan
31.0ms	500×	body	256	nan
16.0ms	472×	body	128	nan
1.0ms	5×	body	4096	nan

Compiler

Compiled 111 to 87 computations (21.6% saved)

Details

analyze260.0ms (7.7%)

sample53.0ms (1.6%)

simplify244.0ms (7.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite21.0ms (0.6%)

series102.0ms (3%)

simplify59.0ms (1.8%)

prune56.0ms (1.7%)

localize9.0ms (0.3%)

rewrite35.0ms (1%)

series90.0ms (2.7%)

simplify81.0ms (2.4%)

prune105.0ms (3.1%)

localize11.0ms (0.3%)

rewrite34.0ms (1%)

series124.0ms (3.7%)

simplify93.0ms (2.8%)

prune118.0ms (3.5%)

regimes67.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.8s (53.2%)

Profiling