Details

analyze42.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample21.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	2×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify162.0ms (7.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4836	17
1	4836	17

prune7.0ms (0.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 14.3b

Counts

2 → 1

Compiler

Compiled 24 to 17 computations (29.2% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 a a) (.f64 b b))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
13.9b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite16.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
7×	`add-sqr-sqrt_binary64_1123`
6×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
5×	`add-log-exp_binary64_1140`
4×	`pow1_binary64_1162` `associate-/l*_binary64_1046` `times-frac_binary64_1107`
3×	`difference-of-squares_binary64_1070` `sqrt-prod_binary64_1117`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `cancel-sign-sub-inv_binary64_1067` `associate-/r*_binary64_1045` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

3 → 52

Calls

3 calls:

7.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
4.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

series96.0ms (4.7%)

Counts

3 → 9

Calls

3 calls:

38.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
35.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
23.0ms	(-.f64 (.f64 a a) (.f64 b b))

simplify65.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5039	1000

prune54.0ms (2.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Merged error: 0b

Counts

62 → 2

Compiler

Compiled 1075 to 365 computations (66% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))
0.0b	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
0.1b	(*.f64 b (/.f64 b a))

rewrite35.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`times-frac_binary64_1107`
71×	`add-sqr-sqrt_binary64_1123`
65×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
22×	`add-exp-log_binary64_1139`
18×	`associate-/r*_binary64_1045`
16×	`add-cbrt-cube_binary64_1137`
13×	`associate-r_binary64_1041`
11×	`associate-/r/_binary64_1047`
9×	`div-exp_binary64_1152`
8×	`pow1_binary64_1162`
7×	`div-inv_binary64_1098`
6×	`associate-/l*_binary64_1046`
5×	`flip--_binary64_1076` `flip3--_binary64_1105` `cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140`
3×	`sqrt-prod_binary64_1117` `associate-l_binary64_1042`
2×	`1-exp_binary64_1145` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `rec-exp_binary64_1151` `unswap-sqr_binary64_1069`
1×	`inv-pow_binary64_1186` `-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `pow-flip_binary64_1175` `pow1/2_binary64_1181`

Counts

4 → 158

Calls

4 calls:

8.0ms	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
7.0ms	(*.f64 b (/.f64 b a))
5.0ms	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))

series121.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
36.0ms	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
32.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))
14.0ms	(*.f64 b (/.f64 b a))

simplify97.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4979	3563
1	4979	3563

prune141.0ms (6.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	170	2	172

Merged error: 0b

Counts

172 → 2

Compiler

Compiled 3550 to 1211 computations (65.9% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
0.1b	(*.f64 b (/.f64 b a))
0.2b	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))

rewrite24.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1123`
21×	`*-un-lft-identity_binary64_1101` `times-frac_binary64_1107`
20×	`add-cube-cbrt_binary64_1136`
17×	`add-exp-log_binary64_1139`
16×	`associate-r_binary64_1041` `associate-l_binary64_1042`
13×	`add-cbrt-cube_binary64_1137`
8×	`pow1_binary64_1162`
6×	`prod-exp_binary64_1150`
5×	`unswap-sqr_binary64_1069`
4×	`cbrt-unprod_binary64_1134`
3×	`add-log-exp_binary64_1140` `sqrt-prod_binary64_1117` `associate-*r/_binary64_1043` `div-exp_binary64_1152`
2×	`*-commutative_binary64_1032` `frac-times_binary64_1111` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `pow-prod-down_binary64_1172` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067` `distribute-rgt-in_binary64_1051`
1×	`1-exp_binary64_1145` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `rec-exp_binary64_1151` `associate-*l/_binary64_1044` `pow1/2_binary64_1181`

Counts

3 → 88

Calls

3 calls:

9.0ms	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))
7.0ms	(*.f64 b (/.f64 b a))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))

series85.0ms (4.2%)

Counts

3 → 9

Calls

3 calls:

39.0ms	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))
33.0ms	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
13.0ms	(*.f64 b (/.f64 b a))

simplify77.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4938	1412
1	4938	1412

prune75.0ms (3.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	97	2	99

Merged error: 0b

Counts

99 → 2

Compiler

Compiled 1703 to 596 computations (65% saved)

regimes125.0ms (6.1%)

Compiler: Compiled 1223 to 761 computations (37.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms (0%)

sample773.0ms (37.7%)

Algorithm

1×

intervals

Results

279.0ms	8000×	body	128	valid
164.0ms	8000×	pre	128	true
2.0ms	113×	pre	128	false

Compiler

Compiled 171 to 108 computations (36.8% saved)

Details

analyze42.0ms (2%)

sample21.0ms (1%)

simplify162.0ms (7.9%)

prune7.0ms (0.4%)

localize7.0ms (0.3%)

rewrite16.0ms (0.8%)

series96.0ms (4.7%)

simplify65.0ms (3.2%)

prune54.0ms (2.7%)

localize11.0ms (0.5%)

rewrite35.0ms (1.7%)

series121.0ms (5.9%)

simplify97.0ms (4.7%)

prune141.0ms (6.9%)

localize8.0ms (0.4%)

rewrite24.0ms (1.2%)

series85.0ms (4.2%)

simplify77.0ms (3.8%)

prune75.0ms (3.7%)

regimes125.0ms (6.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample773.0ms (37.7%)

Profiling