Details

analyze599.0ms (6.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	154
1	43	154
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Symmetry

Compiler

Compiled 16 to 12 computations (25% saved)

sample22.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	13×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune2.0ms (0%)

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

23.4b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a c) (.f64 b d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
23.0b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite87.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

23.2b

Rules

11×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
9×	`times-frac_binary64_1107`
7×	`add-log-exp_binary64_1140`
5×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
4×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`pow1_binary64_1162` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `sum-log_binary64_1192` `+-commutative_binary64_1031`
1×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098`

Counts

3 → 53

Calls

3 calls:

9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 1469 to 193 computations (86.9% saved)

series593.0ms (6.7%)

Error

5.3b

Counts

3 → 63

Calls

3 calls:

323.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
146.0ms	(+.f64 (.f64 a c) (.f64 b d))
84.0ms	(+.f64 (.f64 c c) (.f64 d d))

Compiler

Compiled 2202 to 1388 computations (37% saved)

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4951	2131
1	4951	2131

prune89.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	110	6	116
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	7	117

Error

5.3b

Counts

117 → 7

Compiler

Compiled 2261 to 299 computations (86.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
13.9b	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
26.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
26.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite244.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

95×	`add-sqr-sqrt_binary64_1123`
76×	`times-frac_binary64_1107`
53×	`*-un-lft-identity_binary64_1101`
47×	`add-cube-cbrt_binary64_1136` `sqrt-prod_binary64_1117`
28×	`add-exp-log_binary64_1139`
24×	`associate-l_binary64_1042` `associate-r_binary64_1041`
18×	`add-cbrt-cube_binary64_1137`
15×	`unswap-sqr_binary64_1069`
10×	`sqrt-div_binary64_1118`
9×	`div-exp_binary64_1152`
8×	`pow1_binary64_1162` `prod-exp_binary64_1150`
6×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-/r/_binary64_1047` `associate-/r*_binary64_1045`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `cbrt-unprod_binary64_1134`
3×	`div-inv_binary64_1098` `associate-/l*_binary64_1046`
2×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-/l/_binary64_1048` `1-exp_binary64_1145` `rec-exp_binary64_1151`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `pow-prod-down_binary64_1172` `frac-times_binary64_1111` `associate-l/_binary64_1044` `associate-r/_binary64_1043` `*-commutative_binary64_1032`

Counts

4 → 160

Calls

4 calls:

32.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
10.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 7120 to 1049 computations (85.3% saved)

series1.1s (12.1%)

Error

5.3b

Counts

4 → 96

Calls

4 calls:

410.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
307.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
134.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
131.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 5790 to 3738 computations (35.4% saved)

simplify124.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4965	7451
1	4965	7451

prune233.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	256	7	263

Error

4.8b

Counts

263 → 7

Compiler

Compiled 8277 to 1326 computations (84% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a c) (.f64 b d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.6b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
22.8b	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

rewrite123.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

27×	`add-sqr-sqrt_binary64_1123`
21×	`*-un-lft-identity_binary64_1101`
20×	`add-cube-cbrt_binary64_1136` `times-frac_binary64_1107`
17×	`add-exp-log_binary64_1139`
15×	`associate-r_binary64_1041`
11×	`add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140`
7×	`pow1_binary64_1162`
6×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
4×	`div-exp_binary64_1152` `prod-exp_binary64_1150` `associate-/r/_binary64_1047`
3×	`unswap-sqr_binary64_1069` `associate-l_binary64_1042` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`1-exp_binary64_1145` `rec-exp_binary64_1151` `cbrt-unprod_binary64_1134` `cbrt-undiv_binary64_1135` `frac-times_binary64_1111` `associate-*l/_binary64_1044` `div-inv_binary64_1098` `sum-log_binary64_1192` `+-commutative_binary64_1031`
1×	`pow-prod-down_binary64_1172` `un-div-inv_binary64_1099` `associate-r/_binary64_1043` `-commutative_binary64_1032` `inv-pow_binary64_1186` `pow-flip_binary64_1175` `frac-2neg_binary64_1112` `clear-num_binary64_1100`

Counts

4 → 97

Calls

4 calls:

13.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
6.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 2761 to 650 computations (76.5% saved)

series648.0ms (7.3%)

Error

4.8b

Counts

4 → 75

Calls

4 calls:

300.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
132.0ms	(+.f64 (.f64 a c) (.f64 b d))
88.0ms	(+.f64 (.f64 c c) (.f64 d d))
82.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 2964 to 2009 computations (32.2% saved)

simplify84.0ms (1%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5147	2961

prune119.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	172	7	179

Error

4.8b

Counts

179 → 7

Compiler

Compiled 3512 to 731 computations (79.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

1.9b	(+.f64 (/.f64 b d) (/.f64 a (/.f64 (*.f64 d d) c)))
5.2b	(/.f64 (*.f64 d d) c)
6.3b	(/.f64 a (/.f64 (*.f64 d d) c))

rewrite108.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

38×	`times-frac_binary64_1107`
27×	`*-un-lft-identity_binary64_1101`
21×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123`
17×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`associate-/r*_binary64_1045`
7×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
6×	`div-inv_binary64_1098`
5×	`add-log-exp_binary64_1140`
4×	`associate-/l*_binary64_1046`
3×	`pow1_binary64_1162`
2×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `distribute-lft-out_binary64_1052`
1×	`associate-/r/_binary64_1047` `sum-log_binary64_1192` `frac-add_binary64_1109` `flip3-+_binary64_1104` `flip-+_binary64_1075` `+-commutative_binary64_1031`

Counts

3 → 83

Calls

3 calls:

22.0ms	(+.f64 (/.f64 b d) (/.f64 a (/.f64 (*.f64 d d) c)))
6.0ms	(/.f64 a (/.f64 (*.f64 d d) c))
5.0ms	(/.f64 (*.f64 d d) c)

Compiler

Compiled 1564 to 356 computations (77.2% saved)

series480.0ms (5.4%)

Error

4.8b

Counts

3 → 39

Calls

3 calls:

264.0ms	(+.f64 (/.f64 b d) (/.f64 a (/.f64 (*.f64 d d) c)))
130.0ms	(/.f64 a (/.f64 (*.f64 d d) c))
64.0ms	(/.f64 (*.f64 d d) c)

Compiler

Compiled 1011 to 756 computations (25.2% saved)

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4972	1730
1	4972	1730

prune75.0ms (0.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	1	2	3
Picked	1	0	1
Done	0	3	3
Total	119	10	129

Error

3.2b

Counts

129 → 10

Compiler

Compiled 1757 to 304 computations (82.7% saved)

regimes1.9s (21%)

Accuracy

Total 9.8b remaining (80.1%)

Threshold costs 0b (0%)

Compiler

Compiled 10521 to 6146 computations (41.6% saved)

bsearch100.0ms (1.1%)

Steps

Iters	Range		Point
7	1.1212822598102334e+80	1.7703897453964647e+82	7.162264487896466e+81
10	5.0661212852755664e-135	2.2985265637657406e-119	2.5365321914959593e-134
10	-4.998751043810138e-102	-7.847994106448998e-112	-7.875830746956647e-107
10	-2.2807487878557336e+101	-1.4391149637484194e+91	-7.553879560626287e+93

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	151
1	52	151

Removed

()

end0.0ms (0%)

sample2.0s (22.2%)

Algorithm

1×

intervals

Results

324.0ms	8000×	body	128	valid
19.0ms	497×	body	128	invalid

Compiler

Compiled 2211 to 1277 computations (42.2% saved)

Details

analyze599.0ms (6.8%)

sample22.0ms (0.3%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite87.0ms (1%)

series593.0ms (6.7%)

simplify121.0ms (1.4%)

prune89.0ms (1%)

localize14.0ms (0.2%)

rewrite244.0ms (2.7%)

series1.1s (12.1%)

simplify124.0ms (1.4%)

prune233.0ms (2.6%)

localize11.0ms (0.1%)

rewrite123.0ms (1.4%)

series648.0ms (7.3%)

simplify84.0ms (1%)

prune119.0ms (1.3%)

localize7.0ms (0.1%)

rewrite108.0ms (1.2%)

series480.0ms (5.4%)

simplify61.0ms (0.7%)

prune75.0ms (0.8%)

regimes1.9s (21%)

bsearch100.0ms (1.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (22.2%)

Profiling