Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample18.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify104.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

prune3.0ms (0.1%)

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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite30.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_1101`
26×	`add-sqr-sqrt_binary64_1123`
21×	`distribute-lft-out_binary64_1052`
18×	`times-frac_binary64_1107`
15×	`add-cube-cbrt_binary64_1136`
14×	`sqrt-prod_binary64_1117`
6×	`associate-/r*_binary64_1045`
5×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
4×	`pow1_binary64_1162`
3×	`flip3-+_binary64_1104` `associate-/l*_binary64_1046` `flip-+_binary64_1075`
2×	`associate-/r/_binary64_1047` `sqrt-div_binary64_1118`
1×	`rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181`

Counts

3 → 71

Calls

3 calls:

8.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(sqrt.f64 (+.f64 x 1))

series147.0ms (5.8%)

Counts

3 → 9

Calls

3 calls:

89.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
31.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify92.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4942	1549
1	4942	1549

prune125.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	3	81

Error

Counts

81 → 3

Compiler

Compiled 1324 to 984 computations (25.7% saved)

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 x (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))
0.2b	(pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)
5.9b	(cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))

rewrite74.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`*-un-lft-identity_binary64_1101`
90×	`cbrt-prod_binary64_1132`
74×	`add-sqr-sqrt_binary64_1123`
63×	`times-frac_binary64_1107`
52×	`distribute-lft-out_binary64_1052`
48×	`add-cube-cbrt_binary64_1136`
36×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180`
26×	`sqrt-prod_binary64_1117`
21×	`associate-/r*_binary64_1045`
7×	`add-exp-log_binary64_1139`
6×	`cube-mult_binary64_1131` `add-log-exp_binary64_1140` `cube-div_binary64_1130` `unpow3_binary64_1167` `add-cbrt-cube_binary64_1137` `sqr-pow_binary64_1073`
5×	`pow1_binary64_1162`
4×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `cbrt-div_binary64_1133`
3×	`pow-unpow_binary64_1178` `associate-/l*_binary64_1046`
2×	`associate-/r/_binary64_1047`
1×	`pow-exp_binary64_1169` `rem-cube-cbrt_binary64_1124` `pow1/3_binary64_1183` `pow-pow_binary64_1173` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `pow-to-exp_binary64_1170` `rem-cbrt-cube_binary64_1125`

Counts

4 → 175

Calls

4 calls:

14.0ms	(pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)
13.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))
12.0ms	(/.f64 x (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

series235.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(/.f64 x (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))
64.0ms	(pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)
25.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
24.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))

simplify121.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4988	4178
1	4988	4178

prune273.0ms (10.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	187	3	190

Error

Counts

190 → 3

Compiler

Compiled 3492 to 2685 computations (23.1% saved)

localize12.0ms (0.5%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
3.1b	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_1101`
14×	`add-sqr-sqrt_binary64_1123`
12×	`sqrt-prod_binary64_1117`
7×	`cancel-sign-sub-inv_binary64_1067`
5×	`add-cube-cbrt_binary64_1136`
4×	`difference-of-squares_binary64_1070` `add-log-exp_binary64_1140`
3×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162` `distribute-lft-out--_binary64_1053`
2×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181`

Counts

2 → 41

Calls

2 calls:

8.0ms	(-.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

series47.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

24.0ms	(-.f64 1 (sqrt.f64 (+.f64 x 1)))
23.0ms	(sqrt.f64 (+.f64 x 1))

simplify93.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4925	670
1	4925	670

prune62.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	47	3	50

Error

Counts

50 → 3

Compiler

Compiled 786 to 490 computations (37.7% saved)

regimes72.0ms (2.8%)

Accuracy

Total 0.2b remaining (99.2%)

Threshold costs 0.2b (99.2%)

Compiler

Compiled 626 to 520 computations (16.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample1.0s (39.2%)

Algorithm

1×

intervals

Results

345.0ms	7999×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 321 to 268 computations (16.5% saved)

Details

analyze5.0ms (0.2%)

sample18.0ms (0.7%)

simplify104.0ms (4.1%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

rewrite30.0ms (1.2%)

series147.0ms (5.8%)

simplify92.0ms (3.6%)

prune125.0ms (4.9%)

localize16.0ms (0.6%)

rewrite74.0ms (2.9%)

series235.0ms (9.2%)

simplify121.0ms (4.7%)

prune273.0ms (10.7%)

localize12.0ms (0.5%)

rewrite14.0ms (0.6%)

series47.0ms (1.8%)

simplify93.0ms (3.6%)

prune62.0ms (2.4%)

regimes72.0ms (2.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (39.2%)

Profiling