Details

analyze809.0ms (7.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4810	96
1	4810	96
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample41.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	168×	body	128	valid
7.0ms	28×	body	2048	valid
6.0ms	32×	body	1024	valid
3.0ms	9×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	31×	body	128	nan
1.0ms	8×	body	256	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify333.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (327.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

32.2b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite139.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

31.9b

Rules

24×	`*-un-lft-identity_binary64_1101`
15×	`add-sqr-sqrt_binary64_1123`
14×	`add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
8×	`add-log-exp_binary64_1140`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
5×	`pow1_binary64_1162` `distribute-lft-out_binary64_1052`
4×	`associate-/l*_binary64_1046`
3×	`sqrt-prod_binary64_1117` `associate-/r*_binary64_1045`
2×	`flip3--_binary64_1105` `sqrt-div_binary64_1118` `flip--_binary64_1076` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-/l/_binary64_1048`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `sum-log_binary64_1192` `+-commutative_binary64_1031` `diff-log_binary64_1193` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2053 to 1050 computations (48.9% saved)

series739.0ms (7%)

Error

5.9b

Counts

4 → 72

Calls

4 calls:

194.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
178.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
170.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
134.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3213 to 2441 computations (24% saved)

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5257	2816

prune155.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	132	12	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Error

5.8b

Counts

145 → 12

Compiler

Compiled 3045 to 1607 computations (47.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.9b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.8b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite450.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

66×	`times-frac_binary64_1107`
59×	`add-sqr-sqrt_binary64_1123`
44×	`*-un-lft-identity_binary64_1101`
30×	`add-cube-cbrt_binary64_1136`
27×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
14×	`difference-of-squares_binary64_1070`
13×	`sqrt-prod_binary64_1117` `associate-/l*_binary64_1046`
10×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/r/_binary64_1047`
9×	`associate-/r*_binary64_1045`
7×	`flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053`
6×	`add-log-exp_binary64_1140` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `div-inv_binary64_1098` `cancel-sign-sub-inv_binary64_1067`
5×	`pow1_binary64_1162`
2×	`sqrt-div_binary64_1118` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-/l/_binary64_1048` `diff-log_binary64_1193` `sub-neg_binary64_1094`

Counts

4 → 136

Calls

4 calls:

200.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
15.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 5265 to 2649 computations (49.7% saved)

series954.0ms (9%)

Error

5.8b

Counts

4 → 71

Calls

4 calls:

324.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
277.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
155.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
131.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4275 to 3059 computations (28.4% saved)

simplify120.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5009	6020

prune267.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	209	10	219

Error

5.8b

Counts

219 → 10

Compiler

Compiled 5927 to 3043 computations (48.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite240.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

102×	`times-frac_binary64_1107`
82×	`*-un-lft-identity_binary64_1101`
57×	`add-sqr-sqrt_binary64_1123`
56×	`add-cube-cbrt_binary64_1136`
18×	`associate-/r*_binary64_1045`
15×	`add-exp-log_binary64_1139`
13×	`distribute-lft-out_binary64_1052`
9×	`add-cbrt-cube_binary64_1137` `associate-/r/_binary64_1047`
8×	`add-log-exp_binary64_1140`
7×	`div-exp_binary64_1152`
6×	`pow1_binary64_1162`
5×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `div-inv_binary64_1098`
3×	`sqrt-prod_binary64_1117` `cbrt-undiv_binary64_1135` `associate-/l*_binary64_1046`
2×	`flip3--_binary64_1105` `sqrt-div_binary64_1118` `flip--_binary64_1076` `1-exp_binary64_1145` `rec-exp_binary64_1151`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `sum-log_binary64_1192` `+-commutative_binary64_1031` `diff-log_binary64_1193` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067` `inv-pow_binary64_1186` `pow-flip_binary64_1175` `frac-2neg_binary64_1112` `clear-num_binary64_1100`

Counts

4 → 135

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4590 to 2591 computations (43.6% saved)

series719.0ms (6.8%)

Error

5.8b

Counts

4 → 72

Calls

4 calls:

203.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
160.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
159.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
137.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3483 to 2713 computations (22.1% saved)

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4929	5302
1	4929	5302

prune243.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	207	10	217

Error

5.8b

Counts

217 → 10

Compiler

Compiled 5175 to 2851 computations (44.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite140.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

21×	`add-sqr-sqrt_binary64_1123`
18×	`*-un-lft-identity_binary64_1101`
13×	`add-exp-log_binary64_1139` `add-cube-cbrt_binary64_1136` `associate-r_binary64_1041`
11×	`times-frac_binary64_1107`
9×	`add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140`
7×	`pow1_binary64_1162`
4×	`prod-exp_binary64_1150` `associate-l_binary64_1042`
3×	`sqrt-prod_binary64_1117` `flip3-+_binary64_1104` `flip-+_binary64_1075` `unswap-sqr_binary64_1069`
2×	`flip3--_binary64_1105` `sqrt-div_binary64_1118` `flip--_binary64_1076` `distribute-lft-out_binary64_1052` `div-exp_binary64_1152` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `associate-*l/_binary64_1044`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `sum-log_binary64_1192` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `1-exp_binary64_1145` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135` `un-div-inv_binary64_1099` `associate-r/_binary64_1043` `div-inv_binary64_1098` `-commutative_binary64_1032` `diff-log_binary64_1193` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067`

Counts

4 → 80

Calls

4 calls:

15.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2417 to 1345 computations (44.4% saved)

series736.0ms (6.9%)

Error

5.8b

Counts

4 → 72

Calls

4 calls:

206.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
168.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
163.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
139.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3483 to 2720 computations (21.9% saved)

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4968	2856
1	4968	2856

prune141.0ms (1.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	152	10	162

Error

5.8b

Counts

162 → 10

Compiler

Compiled 3134 to 1735 computations (44.6% saved)

regimes1.2s (11.3%)

Accuracy

Total 1.1b remaining (16.1%)

Threshold costs 0b (0%)

Compiler

Compiled 7512 to 5482 computations (27% saved)

bsearch100.0ms (0.9%)

Steps

Iters	Range	Point
7	9.536573715997247e+107	2.272091706956965e+109	1.2510227225299573e+109
9	1.1761980487950557e-203	1.1901236388873502e-196	1.1519003584921026e-201
7	-5.222027993423419e+93	-4.515317171743753e+91	-5.110132017758097e+93

Iters

Range

Point

9.536573715997247e+107

2.272091706956965e+109

1.2510227225299573e+109

1.1761980487950557e-203

1.1901236388873502e-196

1.1519003584921026e-201

-5.222027993423419e+93

-4.515317171743753e+91

-5.110132017758097e+93

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	147	100
1	147	100

end0.0ms (0%)

sample2.8s (26%)

Algorithm

1×

intervals

Results

275.0ms	1101×	body	2048	valid
266.0ms	5242×	body	128	valid
143.0ms	741×	body	1024	valid
127.0ms	391×	body	4096	valid
52.0ms	348×	body	512	valid
38.0ms	685×	body	128	nan
19.0ms	383×	body	128	invalid
17.0ms	177×	body	256	valid

Compiler

Compiled 1995 to 1450 computations (27.3% saved)

Details

analyze809.0ms (7.6%)

sample41.0ms (0.4%)

simplify333.0ms (3.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite139.0ms (1.3%)

series739.0ms (7%)

simplify67.0ms (0.6%)

prune155.0ms (1.5%)

localize12.0ms (0.1%)

rewrite450.0ms (4.2%)

series954.0ms (9%)

simplify120.0ms (1.1%)

prune267.0ms (2.5%)

localize12.0ms (0.1%)

rewrite240.0ms (2.3%)

series719.0ms (6.8%)

simplify108.0ms (1%)

prune243.0ms (2.3%)

localize12.0ms (0.1%)

rewrite140.0ms (1.3%)

series736.0ms (6.9%)

simplify84.0ms (0.8%)

prune141.0ms (1.3%)

regimes1.2s (11.3%)

bsearch100.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.8s (26%)

Profiling