Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify176.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (167.0ms)

Iter	Nodes	Cost
0	4665	25
1	4665	25

prune7.0ms

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

Merged error: 0.0b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
0.0b	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x)
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
17.4b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1201`
16×	`*-un-lft-identity_binary64_1216`
14×	`add-cube-cbrt_binary64_1187`
10×	`times-frac_binary64_1211`
8×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180` `add-log-exp_binary64_1181`
6×	`pow1_binary64_1162`
4×	`flip-+_binary64_1241` `flip3-+_binary64_1214`
3×	`associate-l_binary64_1276` `associate-r_binary64_1275` `associate-/r_binary64_1279` `associate-/l_binary64_1280`
2×	`associate-*r/_binary64_1277` `associate-/r/_binary64_1281` `associate-/l/_binary64_1282` `difference-of-squares_binary64_1245`
1×	`flip3--_binary64_1215` `sum-log_binary64_1131` `distribute-lft-out--_binary64_1261` `div-exp_binary64_1169` `cbrt-unprod_binary64_1185` `pow-prod-down_binary64_1143` `div-inv_binary64_1217` `clear-num_binary64_1219` `unswap-sqr_binary64_1244` `diff-log_binary64_1132` `cbrt-undiv_binary64_1186` `sub-neg_binary64_1220` `prod-exp_binary64_1167` `*-commutative_binary64_1284` `frac-2neg_binary64_1209` `distribute-lft-in_binary64_1258` `+-commutative_binary64_1283` `flip--_binary64_1242` `distribute-rgt-in_binary64_1259`

Counts

4 → 78

Calls

4 calls:

3.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
11.0ms	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x)
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
7.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

series116.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
27.0ms	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x)
42.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
22.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify101.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5004	2132

prune393.0ms

Filtered

68 candidates to 90 candidates (-32.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	3	91

Merged error: 0b

Counts

91 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
0.1b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
17.3b	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))
17.3b	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac_binary64_1211`
164×	`add-sqr-sqrt_binary64_1201`
162×	`*-un-lft-identity_binary64_1216` `add-cube-cbrt_binary64_1187`
156×	`sqrt-prod_binary64_1195`
27×	`associate-/l*_binary64_1280`
22×	`sqrt-div_binary64_1196`
18×	`associate-/r/_binary64_1281`
12×	`flip-+_binary64_1241` `flip3-+_binary64_1214` `associate-/r*_binary64_1279`
11×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180`
9×	`div-inv_binary64_1217`
6×	`pow1_binary64_1162`
4×	`div-exp_binary64_1169` `cbrt-undiv_binary64_1186` `add-log-exp_binary64_1181`
3×	`associate-/l/_binary64_1282`
2×	`pow1/2_binary64_1152` `clear-num_binary64_1219` `rem-sqrt-square_binary64_1204` `frac-2neg_binary64_1209` `sqrt-pow1_binary64_1197`

Counts

4 → 264

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
8.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
41.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
30.0ms	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))
27.0ms	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

simplify412.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4963	15642
1	4963	15642

prune1.1s

Filtered

150 candidates to 276 candidates (-84.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	276	3	279

Merged error: 0b

Counts

279 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))))
0.0b	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))) x)
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
3.5b	(log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_1216`
24×	`add-sqr-sqrt_binary64_1201`
17×	`add-cube-cbrt_binary64_1187`
16×	`times-frac_binary64_1211`
11×	`pow1_binary64_1162`
8×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180` `distribute-lft-out_binary64_1260`
7×	`log-pow_binary64_1137` `add-log-exp_binary64_1181`
5×	`log-prod_binary64_1134` `associate-/r*_binary64_1279`
3×	`flip-+_binary64_1241` `flip3-+_binary64_1214` `associate-l_binary64_1276` `associate-r_binary64_1275` `associate-/l*_binary64_1280`
2×	`exp-sum_binary64_1175` `associate-*r/_binary64_1277` `associate-/r/_binary64_1281` `associate-/l/_binary64_1282` `distribute-lft-in_binary64_1258` `distribute-rgt-in_binary64_1259` `difference-of-squares_binary64_1245`
1×	`flip3--_binary64_1215` `distribute-lft-out--_binary64_1261` `div-exp_binary64_1169` `cbrt-unprod_binary64_1185` `pow-prod-down_binary64_1143` `div-inv_binary64_1217` `clear-num_binary64_1219` `unswap-sqr_binary64_1244` `exp-prod_binary64_1170` `exp-to-pow_binary64_1156` `diff-log_binary64_1132` `cbrt-undiv_binary64_1186` `sub-neg_binary64_1220` `prod-exp_binary64_1167` `*-commutative_binary64_1284` `frac-2neg_binary64_1209` `rem-log-exp_binary64_1179` `flip--_binary64_1242`

Counts

4 → 91

Calls

4 calls:

8.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))))
14.0ms	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))) x)
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
2.0ms	(log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

series134.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))))
28.0ms	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))) x)
42.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
43.0ms	(log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5201	2444

prune404.0ms

Filtered

73 candidates to 103 candidates (-41.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	103	3	106

Merged error: 0b

Counts

106 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
3.9b	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
4.7b	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac_binary64_1211`
166×	`add-sqr-sqrt_binary64_1201`
163×	`*-un-lft-identity_binary64_1216` `add-cube-cbrt_binary64_1187`
153×	`sqrt-prod_binary64_1195`
30×	`associate-/r*_binary64_1279`
20×	`sqrt-div_binary64_1196`
17×	`associate-/r/_binary64_1281`
13×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180`
12×	`flip-+_binary64_1241` `flip3-+_binary64_1214`
9×	`div-inv_binary64_1217` `associate-/l*_binary64_1280`
7×	`pow1_binary64_1162`
4×	`div-exp_binary64_1169` `cbrt-undiv_binary64_1186` `add-log-exp_binary64_1181` `associate-/l/_binary64_1282`
3×	`associate-l_binary64_1276` `associate-r_binary64_1275`
2×	`clear-num_binary64_1219` `associate-*r/_binary64_1277` `frac-2neg_binary64_1209`
1×	`cbrt-unprod_binary64_1185` `pow-prod-down_binary64_1143` `pow1/2_binary64_1152` `rem-sqrt-square_binary64_1204` `unswap-sqr_binary64_1244` `prod-exp_binary64_1167` `*-commutative_binary64_1284` `distribute-lft-in_binary64_1258` `distribute-rgt-in_binary64_1259` `sqrt-pow1_binary64_1197`

Counts

4 → 271

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))
10.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
8.0ms	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
15.0ms	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))))

series121.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))
38.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
41.0ms	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
24.0ms	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))))

simplify209.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4924	14036
1	4924	14036

prune197.0ms

Filtered: 157 candidates to 283 candidates (-80.3%)

Details

analyze5.0ms

sample22.0ms

simplify176.0ms

prune7.0ms

localize22.0ms

rewrite29.0ms

series116.0ms

simplify101.0ms

prune393.0ms

localize21.0ms

rewrite45.0ms

series120.0ms

simplify412.0ms

prune1.1s

localize30.0ms

rewrite33.0ms

series134.0ms

simplify110.0ms

prune404.0ms

localize21.0ms

rewrite53.0ms

series121.0ms

simplify209.0ms

prune197.0ms

Profiling