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)

sample29.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	61×	body	1024	valid
6.0ms	145×	body	128	valid
4.0ms	31×	body	512	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify100.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune3.0ms (0.1%)

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

18.2b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
3.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite74.0ms (1.5%)

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:

43.0ms	(-.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))

series82.0ms (1.7%)

Counts

4 → 18

Calls

4 calls:

26.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
25.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
18.0ms	(sqrt.f64 (+.f64 x 1))
13.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 370 to 323 computations (12.7% saved)

simplify96.0ms (2%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4860	3341
1	4860	3341

prune236.0ms (4.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	196	11	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	197	11	208

Error

17.6b

Counts

208 → 11

Compiler

Compiled 3647 to 2722 computations (25.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.4b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite52.0ms (1.1%)

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:

18.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.0ms	(sqrt.f64 (+.f64 1 x))

series139.0ms (2.9%)

Counts

4 → 18

Calls

4 calls:

59.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
31.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
30.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
18.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 528 to 419 computations (20.6% saved)

simplify66.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5277	2138

prune144.0ms (3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	138	4	142

Error

0.2b

Counts

142 → 4

Compiler

Compiled 2619 to 1687 computations (35.6% saved)

localize9.0ms (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))))
0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite70.0ms (1.4%)

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:

20.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 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)))

series115.0ms (2.4%)

Counts

4 → 15

Calls

4 calls:

49.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
28.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
23.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
15.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 386 to 331 computations (14.2% saved)

simplify99.0ms (2%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4965	3678
1	4965	3678

prune255.0ms (5.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	175	10	185

Error

0.0b

Counts

185 → 10

Compiler

Compiled 4184 to 2893 computations (30.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_1123`
22×	`*-un-lft-identity_binary64_1101`
18×	`add-cube-cbrt_binary64_1136`
13×	`associate-r_binary64_1041`
12×	`add-exp-log_binary64_1139` `flip3-+_binary64_1104` `flip-+_binary64_1075`
10×	`associate-r/_binary64_1043` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118` `associate-l/_binary64_1044`
9×	`pow1_binary64_1162` `sqrt-prod_binary64_1117` `times-frac_binary64_1107`
8×	`frac-add_binary64_1109`
7×	`associate-l_binary64_1042`
6×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
4×	`unswap-sqr_binary64_1069`
3×	`associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out_binary64_1052` `pow-prod-down_binary64_1172` `div-exp_binary64_1152`
1×	`inv-pow_binary64_1186` `1-exp_binary64_1145` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `div-inv_binary64_1098` `rec-exp_binary64_1151` `+-commutative_binary64_1031` `cbrt-undiv_binary64_1135` `pow-flip_binary64_1175`

Counts

4 → 102

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (.f64 x (sqrt.f64 (+.f64 x 1)))))
9.0ms	(+.f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (.f64 x (sqrt.f64 (+.f64 x 1))))
8.0ms	(*.f64 (+.f64 x 1) (sqrt.f64 x))
7.0ms	(*.f64 x (sqrt.f64 (+.f64 x 1)))

series130.0ms (2.7%)

Counts

4 → 15

Calls

4 calls:

50.0ms	(/.f64 1 (+.f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (.f64 x (sqrt.f64 (+.f64 x 1)))))
35.0ms	(+.f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (.f64 x (sqrt.f64 (+.f64 x 1))))
25.0ms	(*.f64 x (sqrt.f64 (+.f64 x 1)))
19.0ms	(*.f64 (+.f64 x 1) (sqrt.f64 x))

Compiler

Compiled 410 to 342 computations (16.6% saved)

simplify87.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4986	2426
1	4986	2426

prune134.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Error

Counts

127 → 8

Compiler

Compiled 2620 to 1703 computations (35% saved)

regimes503.0ms (10.4%)

Accuracy

Total 0.6b remaining (99.5%)

Threshold costs 0.6b (99.5%)

Compiler

Compiled 3556 to 2786 computations (21.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	22
1	15	22

end0.0ms (0%)

sample2.3s (48.4%)

Algorithm

1×

intervals

Results

325.0ms	2192×	body	1024	valid
176.0ms	4258×	body	128	valid
112.0ms	1035×	body	512	valid
42.0ms	515×	body	256	valid

Compiler

Compiled 1807 to 1416 computations (21.6% saved)

Details

analyze2.0ms (0%)

sample29.0ms (0.6%)

simplify100.0ms (2.1%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite74.0ms (1.5%)

series82.0ms (1.7%)

simplify96.0ms (2%)

prune236.0ms (4.9%)

localize7.0ms (0.2%)

rewrite52.0ms (1.1%)

series139.0ms (2.9%)

simplify66.0ms (1.4%)

prune144.0ms (3%)

localize9.0ms (0.2%)

rewrite70.0ms (1.4%)

series115.0ms (2.4%)

simplify99.0ms (2%)

prune255.0ms (5.3%)

localize9.0ms (0.2%)

rewrite44.0ms (0.9%)

series130.0ms (2.7%)

simplify87.0ms (1.8%)

prune134.0ms (2.8%)

regimes503.0ms (10.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (48.4%)

Profiling