Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample41.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	57×	body	1024	valid
9.0ms	143×	body	128	valid
7.0ms	39×	body	512	valid
2.0ms	17×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify108.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune3.0ms (0%)

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

Error

19.9b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 1 (sqrt.f64 x))
2.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite98.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64_1123`
118×	`times-frac_binary64_1107`
117×	`*-un-lft-identity_binary64_1101`
76×	`sqrt-prod_binary64_1117`
56×	`add-cube-cbrt_binary64_1136`
27×	`cancel-sign-sub-inv_binary64_1067`
25×	`difference-of-squares_binary64_1070`
13×	`distribute-lft-out--_binary64_1053` `associate-/r*_binary64_1045`
12×	`add-exp-log_binary64_1139`
11×	`distribute-lft-out_binary64_1052`
9×	`pow1_binary64_1162`
8×	`add-cbrt-cube_binary64_1137`
7×	`div-inv_binary64_1098`
6×	`add-log-exp_binary64_1140` `associate-/l*_binary64_1046` `sqrt-div_binary64_1118` `pow-flip_binary64_1175`
4×	`associate-/r/_binary64_1047` `div-exp_binary64_1152`
3×	`sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181`
2×	`inv-pow_binary64_1186` `1-exp_binary64_1145` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `flip--_binary64_1076` `flip3--_binary64_1105` `frac-sub_binary64_1110`

Counts

4 → 189

Calls

4 calls:

41.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
7.0ms	(/.f64 1 (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))

series142.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
31.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
29.0ms	(/.f64 1 (sqrt.f64 x))
17.0ms	(sqrt.f64 (+.f64 x 1))

simplify138.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4945	3696
1	4945	3696

prune443.0ms (5.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	188	13	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	13	202

Error

19.3b

Counts

202 → 13

Compiler

Compiled 3859 to 2842 computations (26.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
2.0b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_1123`
42×	`sqrt-prod_binary64_1117`
38×	`*-un-lft-identity_binary64_1101`
13×	`add-cube-cbrt_binary64_1136`
12×	`difference-of-squares_binary64_1070`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`associate-/l*_binary64_1046` `times-frac_binary64_1107`
9×	`pow1_binary64_1162` `distribute-lft-out--_binary64_1053`
7×	`associate-r_binary64_1041`
6×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `associate-l_binary64_1042` `cancel-sign-sub-inv_binary64_1067`
5×	`distribute-lft-out_binary64_1052`
4×	`associate-*r/_binary64_1043` `unswap-sqr_binary64_1069`
3×	`sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `pow1/2_binary64_1181`
2×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`diff-log_binary64_1193` `-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `div-inv_binary64_1098` `sqrt-unprod_binary64_1121` `associate-/r_binary64_1045` `div-sub_binary64_1106`

Counts

4 → 113

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

series251.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
67.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
53.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
16.0ms	(sqrt.f64 (+.f64 1 x))

simplify137.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4956	2693
1	4956	2693

prune220.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	134	4	138

Error

0.2b

Counts

138 → 4

Compiler

Compiled 2897 to 1877 computations (35.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite136.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_1101`
78×	`times-frac_binary64_1107`
55×	`sqrt-prod_binary64_1117`
47×	`add-sqr-sqrt_binary64_1123`
45×	`distribute-lft-out_binary64_1052`
39×	`add-cube-cbrt_binary64_1136`
32×	`add-exp-log_binary64_1139`
27×	`associate-/l*_binary64_1046`
20×	`add-cbrt-cube_binary64_1137`
14×	`div-exp_binary64_1152`
9×	`pow1_binary64_1162`
8×	`associate-/r/_binary64_1047`
7×	`associate-r_binary64_1041` `cbrt-undiv_binary64_1135` `associate-/r*_binary64_1045`
6×	`add-log-exp_binary64_1140` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-l_binary64_1042`
5×	`prod-exp_binary64_1150`
4×	`associate-*r/_binary64_1043` `div-inv_binary64_1098` `sqrt-div_binary64_1118` `unswap-sqr_binary64_1069`
3×	`1-exp_binary64_1145` `cbrt-unprod_binary64_1134` `rec-exp_binary64_1151` `pow-prod-down_binary64_1172`
2×	`frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `pow1/2_binary64_1181`
1×	`inv-pow_binary64_1186` `*-commutative_binary64_1032` `sum-log_binary64_1192` `associate-/l/_binary64_1048` `+-commutative_binary64_1031` `sqrt-unprod_binary64_1121` `pow-flip_binary64_1175`

Counts

4 → 166

Calls

4 calls:

46.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
21.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
18.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
16.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series231.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
52.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
45.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
39.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify111.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4952	4177
1	4952	4177

prune325.0ms (4.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	169	9	178
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	172	10	182

Error

0.0b

Counts

182 → 10

Compiler

Compiled 4468 to 3062 computations (31.5% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite87.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64_1107`
159×	`*-un-lft-identity_binary64_1101`
156×	`add-sqr-sqrt_binary64_1123`
119×	`add-cube-cbrt_binary64_1136`
87×	`sqrt-prod_binary64_1117`
49×	`distribute-lft-out_binary64_1052`
21×	`associate-/l*_binary64_1046`
20×	`associate-/r/_binary64_1047`
19×	`add-exp-log_binary64_1139`
13×	`add-cbrt-cube_binary64_1137`
12×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
11×	`associate-/r*_binary64_1045`
10×	`div-inv_binary64_1098`
9×	`pow1_binary64_1162`
8×	`div-exp_binary64_1152`
7×	`associate-r_binary64_1041`
6×	`add-log-exp_binary64_1140` `associate-l_binary64_1042`
4×	`sqrt-div_binary64_1118` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069`
3×	`pow-prod-down_binary64_1172`
2×	`1-exp_binary64_1145` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-*r/_binary64_1043` `rec-exp_binary64_1151` `pow1/2_binary64_1181`
1×	`inv-pow_binary64_1186` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sum-log_binary64_1192` `associate-/l/_binary64_1048` `+-commutative_binary64_1031` `sqrt-unprod_binary64_1121` `pow-flip_binary64_1175`

Counts

4 → 252

Calls

4 calls:

19.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
13.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

series192.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
54.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
25.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
24.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

simplify213.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4947	9729
1	4947	9729

prune687.0ms (9.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	261	3	264
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	263	11	274

Error

Counts

274 → 11

Compiler

Compiled 7549 to 5393 computations (28.6% saved)

regimes450.0ms (6%)

Accuracy

Total 0.3b remaining (98.6%)

Threshold costs 0.3b (98.6%)

Compiler

Compiled 3432 to 2720 computations (20.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample3.4s (45.3%)

Algorithm

1×

intervals

Results

488.0ms	2266×	body	1024	valid
239.0ms	4241×	body	128	valid
160.0ms	987×	body	512	valid
53.0ms	506×	body	256	valid

Compiler

Compiled 1747 to 1386 computations (20.7% saved)

Details

analyze3.0ms (0%)

sample41.0ms (0.5%)

simplify108.0ms (1.4%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite98.0ms (1.3%)

series142.0ms (1.9%)

simplify138.0ms (1.8%)

prune443.0ms (5.9%)

localize11.0ms (0.2%)

rewrite48.0ms (0.6%)

series251.0ms (3.3%)

simplify137.0ms (1.8%)

prune220.0ms (2.9%)

localize17.0ms (0.2%)

rewrite136.0ms (1.8%)

series231.0ms (3.1%)

simplify111.0ms (1.5%)

prune325.0ms (4.3%)

localize21.0ms (0.3%)

rewrite87.0ms (1.2%)

series192.0ms (2.5%)

simplify213.0ms (2.8%)

prune687.0ms (9.1%)

regimes450.0ms (6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.4s (45.3%)

Profiling