Details

analyze808.0ms (8.4%)

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

Symmetry

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample40.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	166×	body	128	valid
7.0ms	31×	body	2048	valid
6.0ms	31×	body	1024	valid
4.0ms	13×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	21×	body	128	nan
1.0ms	12×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify338.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (333.0ms)

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

35.4b

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)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite143.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

35.2b

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:

12.0ms	(/.f64 (+.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)))))
5.0ms	(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)

series679.0ms (7.1%)

Error

5.5b

Counts

4 → 70

Calls

4 calls:

185.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
167.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
143.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3077 to 2341 computations (23.9% saved)

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5243	2757

prune147.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Error

5.3b

Counts

143 → 9

Compiler

Compiled 2901 to 1519 computations (47.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.8b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
11.2b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite266.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

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:

16.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
13.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
10.0ms	(-.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)

series994.0ms (10.4%)

Error

5.3b

Counts

4 → 70

Calls

4 calls:

347.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
314.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
141.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4287 to 3065 computations (28.5% saved)

simplify106.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4949	6059
1	4949	6059

prune273.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	207	8	215

Error

5.3b

Counts

215 → 8

Compiler

Compiled 5879 to 3030 computations (48.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite153.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

39×	`add-sqr-sqrt_binary64_1123`
28×	`*-un-lft-identity_binary64_1101`
18×	`add-cube-cbrt_binary64_1136` `times-frac_binary64_1107`
11×	`sqrt-prod_binary64_1117`
10×	`difference-of-squares_binary64_1070`
8×	`add-log-exp_binary64_1140`
7×	`cancel-sign-sub-inv_binary64_1067`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
5×	`pow1_binary64_1162` `distribute-lft-out--_binary64_1053`
4×	`flip3--_binary64_1105` `flip--_binary64_1076`
3×	`associate-/l*_binary64_1046`
2×	`sqrt-div_binary64_1118` `diff-log_binary64_1193` `sub-neg_binary64_1094` `associate-/r/_binary64_1047`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098`

Counts

4 → 88

Calls

4 calls:

9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2944 to 1670 computations (43.3% saved)

series780.0ms (8.1%)

Error

5.3b

Counts

4 → 71

Calls

4 calls:

268.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
165.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
158.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3942 to 3126 computations (20.7% saved)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4994	3480
1	4994	3480

prune181.0ms (1.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	159	8	167

Error

5.3b

Counts

167 → 8

Compiler

Compiled 4049 to 2384 computations (41.1% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 2 (/.f64 c b))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

14×	`add-sqr-sqrt_binary64_1123`
13×	`associate-r_binary64_1041`
10×	`times-frac_binary64_1107`
9×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`pow1_binary64_1162` `associate-l_binary64_1042`
2×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069`
1×	`pow-prod-down_binary64_1172` `div-exp_binary64_1152` `add-log-exp_binary64_1140` `cbrt-undiv_binary64_1135` `associate-r/_binary64_1043` `div-inv_binary64_1098` `-commutative_binary64_1032`

Counts

1 → 32

Calls

1 calls:

8.0ms

(*.f64 2 (/.f64 c b))

Compiler

Compiled 437 to 259 computations (40.7% saved)

series64.0ms (0.7%)

Error

5.3b

Counts

1 → 6

Calls

1 calls:

60.0ms

(*.f64 2 (/.f64 c b))

Compiler

Compiled 126 to 124 computations (1.6% saved)

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4974	369
1	4974	369

prune25.0ms (0.3%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	36	10	46

Error

5.3b

Counts

46 → 10

Compiler

Compiled 432 to 248 computations (42.6% saved)

regimes1.4s (14.4%)

Accuracy

Total 1.5b remaining (22.4%)

Threshold costs 0b (0%)

Compiler

Compiled 7836 to 5726 computations (26.9% saved)

bsearch119.0ms (1.2%)

Steps

Iters	Range	Point
8	2.1003686100253152e+22	1.822742175881618e+25	1.8042819818410436e+25
9	5.722025691574056e-255	8.551686186721416e-249	1.5126179102014787e-251
10	-2.151171211119653e+160	-1.0565256005736422e+149	-1.5124621562905613e+151

Iters

Range

Point

2.1003686100253152e+22

1.822742175881618e+25

1.8042819818410436e+25

5.722025691574056e-255

8.551686186721416e-249

1.5126179102014787e-251

-2.151171211119653e+160

-1.0565256005736422e+149

-1.5124621562905613e+151

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	108	95
1	108	95

Removed

()

end0.0ms (0%)

sample2.8s (29%)

Algorithm

1×

intervals

Results

267.0ms	5262×	body	128	valid
267.0ms	1091×	body	2048	valid
140.0ms	710×	body	1024	valid
120.0ms	398×	body	4096	valid
53.0ms	357×	body	512	valid
31.0ms	674×	body	128	nan
21.0ms	378×	body	128	invalid
17.0ms	182×	body	256	valid

Compiler

Compiled 2073 to 1508 computations (27.3% saved)

Details

analyze808.0ms (8.4%)

sample40.0ms (0.4%)

simplify338.0ms (3.5%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite143.0ms (1.5%)

series679.0ms (7.1%)

simplify69.0ms (0.7%)

prune147.0ms (1.5%)

localize12.0ms (0.1%)

rewrite266.0ms (2.8%)

series994.0ms (10.4%)

simplify106.0ms (1.1%)

prune273.0ms (2.8%)

localize13.0ms (0.1%)

rewrite153.0ms (1.6%)

series780.0ms (8.1%)

simplify77.0ms (0.8%)

prune181.0ms (1.9%)

localize5.0ms (0%)

rewrite34.0ms (0.3%)

series64.0ms (0.7%)

simplify84.0ms (0.9%)

prune25.0ms (0.3%)

regimes1.4s (14.4%)

bsearch119.0ms (1.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.8s (29%)

Profiling