Details

analyze2.0ms (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)

sample32.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	77×	body	1024	valid
10.0ms	128×	body	128	valid
3.0ms	30×	body	512	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify101.0ms (1.9%)

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

20.5b

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))
3.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite78.0ms (1.4%)

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:

45.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series103.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
34.0ms	(/.f64 1 (sqrt.f64 x))
18.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify105.0ms (2%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4945	3696
1	4945	3696

prune246.0ms (4.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	192	9	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	193	9	202

Error

19.8b

Counts

202 → 9

Compiler

Compiled 3762 to 2762 computations (26.6% saved)

localize7.0ms (0.1%)

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)))
3.3b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite53.0ms (1%)

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:

19.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(*.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))

series168.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
38.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
25.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
14.0ms	(sqrt.f64 (+.f64 1 x))

simplify79.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4956	2693
1	4956	2693

prune146.0ms (2.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	131	3	134

Error

0.3b

Counts

134 → 3

Compiler

Compiled 2888 to 1874 computations (35.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite72.0ms (1.3%)

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:

22.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series169.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
29.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
28.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
25.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4952	4177
1	4952	4177

prune262.0ms (4.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	170	8	178
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	171	10	181

Error

Counts

181 → 10

Compiler

Compiled 4471 to 3066 computations (31.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite63.0ms (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:

14.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
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))))

series180.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
41.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
32.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
22.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

simplify166.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4947	9729
1	4947	9729

prune481.0ms (9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	265	9	274

Error

Counts

274 → 9

Compiler

Compiled 7549 to 5392 computations (28.6% saved)

regimes267.0ms (5%)

Accuracy

Total 0.3b remaining (98%)

Threshold costs 0.3b (98%)

Compiler

Compiled 3244 to 2572 computations (20.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample2.5s (45.8%)

Algorithm

1×

intervals

Results

367.0ms	4348×	body	128	valid
333.0ms	2139×	body	1024	valid
115.0ms	1028×	body	512	valid
36.0ms	485×	body	256	valid

Compiler

Compiled 1653 to 1311 computations (20.7% saved)

Details

analyze2.0ms (0%)

sample32.0ms (0.6%)

simplify101.0ms (1.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite78.0ms (1.4%)

series103.0ms (1.9%)

simplify105.0ms (2%)

prune246.0ms (4.6%)

localize7.0ms (0.1%)

rewrite53.0ms (1%)

series168.0ms (3.1%)

simplify79.0ms (1.5%)

prune146.0ms (2.7%)

localize8.0ms (0.2%)

rewrite72.0ms (1.3%)

series169.0ms (3.2%)

simplify93.0ms (1.7%)

prune262.0ms (4.9%)

localize10.0ms (0.2%)

rewrite63.0ms (1.2%)

series180.0ms (3.4%)

simplify166.0ms (3.1%)

prune481.0ms (9%)

regimes267.0ms (5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.5s (45.8%)

Profiling