Details

analyze267.0ms (9.1%)

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)

sample57.0ms (1.9%)

Algorithm

1×

intervals

Results

20.0ms	131×	body	2048	nan
11.0ms	256×	body	128	valid
9.0ms	74×	body	1024	nan
4.0ms	40×	body	512	nan
2.0ms	24×	body	256	nan
1.0ms	17×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify239.0ms (8.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (148.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14

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

Merged error: 29.6b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.0b	(-.f64 (*.f64 x x) 1)
27.6b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite28.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1101`
10×	`add-sqr-sqrt_binary64_1123`
8×	`add-log-exp_binary64_1140`
7×	`add-cube-cbrt_binary64_1136`
6×	`pow1_binary64_1162` `sqrt-prod_binary64_1117`
5×	`add-exp-log_binary64_1139`
4×	`difference-of-squares_binary64_1070` `add-cbrt-cube_binary64_1137` `log-prod_binary64_1187`
3×	`cancel-sign-sub-inv_binary64_1067`
2×	`distribute-lft-out_binary64_1052` `difference-of-sqr-1_binary64_1071` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `sqrt-div_binary64_1118` `flip-+_binary64_1075` `log-div_binary64_1188`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `sum-log_binary64_1192` `sub-neg_binary64_1094` `rem-log-exp_binary64_1142` `sqrt-pow1_binary64_1119` `+-commutative_binary64_1031` `log-pow_binary64_1190` `pow1/2_binary64_1181`

Counts

4 → 62

Calls

4 calls:

8.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
7.0ms	(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)

series123.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
30.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
24.0ms	(-.f64 (*.f64 x x) 1)
22.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify65.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4949	1098
1	4949	1098

prune65.0ms (2.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	2	75

Merged error: 0.0b

Counts

75 → 2

Compiler

Compiled 1063 to 696 computations (34.5% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1123`
15×	`sqrt-prod_binary64_1117`
13×	`*-un-lft-identity_binary64_1101`
12×	`sqrt-div_binary64_1118`
10×	`associate-r_binary64_1041`
8×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
7×	`associate-l_binary64_1042`
6×	`add-exp-log_binary64_1139`
5×	`add-log-exp_binary64_1140` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `flip-+_binary64_1075`
4×	`frac-times_binary64_1111` `unswap-sqr_binary64_1069`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `log-prod_binary64_1187` `pow-prod-down_binary64_1172`
2×	`difference-of-squares_binary64_1070` `sqrt-pow1_binary64_1119` `associate-r/_binary64_1043` `log-div_binary64_1188` `associate-l/_binary64_1044` `pow1/2_binary64_1181`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `rem-log-exp_binary64_1142` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `+-commutative_binary64_1031` `log-pow_binary64_1190` `sqrt-unprod_binary64_1121`

Counts

3 → 68

Calls

3 calls:

14.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
2.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))

series111.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
34.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
33.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify74.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4977	1681
1	4977	1681

prune85.0ms (2.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	77	2	79

Merged error: 0.0b

Counts

79 → 2

Compiler

Compiled 1507 to 1143 computations (24.2% saved)

regimes43.0ms (1.4%)

Compiler: Compiled 240 to 193 computations (19.6% 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%)

sample1.7s (59.1%)

Algorithm

1×

intervals

Results

628.0ms	3971×	body	2048	nan
347.0ms	8000×	body	128	valid
242.0ms	1911×	body	1024	nan
90.0ms	982×	body	512	nan
34.0ms	507×	body	256	nan
17.0ms	506×	body	128	nan
1.0ms	6×	body	4096	nan

Compiler

Compiled 90 to 74 computations (17.8% saved)

Details

analyze267.0ms (9.1%)

sample57.0ms (1.9%)

simplify239.0ms (8.1%)

prune5.0ms (0.2%)

localize7.0ms (0.2%)

rewrite28.0ms (1%)

series123.0ms (4.2%)

simplify65.0ms (2.2%)

prune65.0ms (2.2%)

localize9.0ms (0.3%)

rewrite25.0ms (0.8%)

series111.0ms (3.8%)

simplify74.0ms (2.5%)

prune85.0ms (2.9%)

regimes43.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.7s (59.1%)

Profiling