Details

analyze806.0ms (0.4%)

Algorithm

1×

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample65.0ms (0%)

Algorithm

1×

intervals

Results

13.0ms	38×	body	1024	valid
11.0ms	162×	body	128	valid
10.0ms	36×	body	1024	nan
7.0ms	34×	body	512	valid
4.0ms	58×	body	128	nan
3.0ms	20×	body	256	valid
3.0ms	9×	body	512	nan
1.0ms	8×	body	256	nan
1.0ms	2×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify157.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5192	41

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

46.7b

Counts

2 → 1

Compiler

Compiled 27 to 20 computations (25.9% saved)

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t))))
0.0b	(.f64 2 (.f64 t t))
0.0b	(+.f64 (.f64 l l) (.f64 2 (*.f64 t t)))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
14.7b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.4b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite65.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_100`
13×	`sqrt-prod_binary64_94`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
7×	`pow1_binary64_139`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `associate-r_binary64_18` `flip--_binary64_53`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `associate--l+_binary64_15` `unswap-sqr_binary64_46` `associate-/r/_binary64_24`
1×	`distribute-lft-in_binary64_27` `-commutative_binary64_9` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l_binary64_23` `pow-prod-down_binary64_149` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71`

Counts

4 → 80

Calls

8 calls:

20.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
16.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
15.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
5.0ms	(*.f64 (sqrt.f64 2) t)
0.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

series4.3s (2.2%)

Counts

4 → 64

Calls

4 calls:

2.2s	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
1.3s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
761.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
36.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 7916 to 6682 computations (15.6% saved)

simplify84.0ms (0%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5111	8470

prune1.1s (0.6%)

Pruning

82 alts after pruning (81 fresh and 1 done)

	Pruned	Kept	Total
New	63	81	144
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	63	82	145

Error

5.3b

Counts

145 → 82

Compiler

Compiled 10280 to 7053 computations (31.4% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))))
0.0b	(.f64 4 (/.f64 (.f64 t t) x))
0.0b	(.f64 2 (/.f64 (.f64 l l) x))
0.0b	(.f64 2 (.f64 t t))
2.5b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
6.2b	(/.f64 (*.f64 l l) x)
9.5b	(/.f64 (*.f64 t t) x)
28.4b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `sqrt-div_binary64_95`
3×	`sqrt-prod_binary64_94` `flip-+_binary64_52` `flip3-+_binary64_81`
2×	`frac-add_binary64_86` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-r/_binary64_20` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158` `sum-log_binary64_169`

Counts

4 → 70

Calls

8 calls:

13.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
7.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
7.0ms	(/.f64 (*.f64 t t) x)
5.0ms	(/.f64 (*.f64 l l) x)
0.0ms	(.f64 2 (.f64 t t))

series849.0ms (0.4%)

Counts

4 → 46

Calls

4 calls:

568.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
146.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
69.0ms	(/.f64 (*.f64 l l) x)
65.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 2911 to 2463 computations (15.4% saved)

simplify107.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4948	3200
1	4948	3200

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

1.0b	(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
1.0b	(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
10×	`sqrt-prod_binary64_94`
6×	`associate-l_binary64_19` `associate-r_binary64_18`
5×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
4×	`unswap-sqr_binary64_46`
3×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow-prod-down_binary64_149`
2×	`sqrt-pow1_binary64_96` `pow1/2_binary64_158`
1×	`*-commutative_binary64_9` `add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `sqrt-unprod_binary64_98`

Counts

1 → 30

Calls

2 calls:

7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
0.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))

series0.0ms (0%)

Counts

1 → 0

Calls

1 calls:

0.0ms

(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))

simplify59.0ms (0%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4861	314
1	4861	314

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b	(*.f64 t (sqrt.f64 2))
0.2b	(/.f64 1 (-.f64 (+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (.f64 l l) (-.f64 x 1))) (.f64 l l)))
0.0b	(.f64 (/.f64 x (-.f64 x 1)) (.f64 l l))
0.0b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (.f64 l l) (-.f64 x 1))) (.f64 l l)))))
0.6b	(+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (*.f64 l l) (-.f64 x 1)))
2.5b	(sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (.f64 l l) (-.f64 x 1))) (.f64 l l))))
6.2b	(/.f64 (*.f64 l l) (-.f64 x 1))
15.4b	(-.f64 (+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (.f64 l l) (-.f64 x 1))) (.f64 l l))

rewrite79.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_100`
21×	`times-frac_binary64_84` `*-un-lft-identity_binary64_78`
18×	`sqrt-prod_binary64_94`
14×	`add-cube-cbrt_binary64_113`
11×	`add-log-exp_binary64_117`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`difference-of-squares_binary64_47`
7×	`associate-/r*_binary64_22`
6×	`pow1_binary64_139`
4×	`associate-/r/_binary64_24`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `flip--_binary64_53`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `distribute-lft-out--_binary64_30` `diff-log_binary64_170` `div-inv_binary64_75` `difference-of-sqr-1_binary64_48` `sum-log_binary64_169`
1×	`+-commutative_binary64_8` `frac-add_binary64_86` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `inv-pow_binary64_163` `flip-+_binary64_52` `frac-2neg_binary64_89` `associate--l+_binary64_15` `pow-flip_binary64_152` `associate-/l_binary64_23` `associate-l/_binary64_21` `sqrt-div_binary64_95` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 91

Calls

8 calls:

24.0ms	(sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (.f64 l l) (-.f64 x 1))) (.f64 l l))))
20.0ms	(-.f64 (+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (.f64 l l) (-.f64 x 1))) (.f64 l l))
16.0ms	(+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (*.f64 l l) (-.f64 x 1)))
7.0ms	(/.f64 (*.f64 l l) (-.f64 x 1))
0.0ms	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (.f64 l l) (-.f64 x 1))) (.f64 l l)))))

series666.0ms (0.3%)

Counts

4 → 37

Calls

4 calls:

245.0ms	(sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (.f64 l l) (-.f64 x 1))) (.f64 l l))))
190.0ms	(-.f64 (+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (.f64 l l) (-.f64 x 1))) (.f64 l l))
148.0ms	(+.f64 (.f64 (/.f64 x (-.f64 x 1)) (.f64 l l)) (/.f64 (*.f64 l l) (-.f64 x 1)))
82.0ms	(/.f64 (*.f64 l l) (-.f64 x 1))

Compiler

Compiled 1548 to 1327 computations (14.3% saved)

simplify97.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4954	3426
1	4954	3426

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 2 (.f64 t t))
0.0b	(.f64 2 (.f64 t t))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
14.7b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.4b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
21.4b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
21.4b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))))

rewrite100.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-pow1_binary64_96` `sqrt-div_binary64_95`
22×	`pow1_binary64_139`
11×	`pow1/2_binary64_158`
9×	`flip3--_binary64_82` `flip--_binary64_53`
8×	`add-sqr-sqrt_binary64_100`
7×	`sqrt-prod_binary64_94`
6×	`add-log-exp_binary64_117` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`pow-prod-up_binary64_148`
4×	`add-cbrt-cube_binary64_114` `frac-times_binary64_88` `add-exp-log_binary64_116`
3×	`pow-sqr_binary64_51` `rem-sqrt-square_binary64_91` `pow-prod-down_binary64_149`
2×	`associate--l+_binary64_15` `associate-l/_binary64_21` `associate-r/_binary64_20`
1×	`pow2_binary64_159` `distribute-lft-in_binary64_27` `diff-log_binary64_170` `distribute-rgt-in_binary64_28` `cancel-sign-sub-inv_binary64_44` `pow-plus_binary64_141` `sub-neg_binary64_71`

Counts

4 → 76

Calls

8 calls:

34.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))))
21.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
16.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
15.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
0.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

series3.8s (2%)

Counts

4 → 75

Calls

4 calls:

1.3s	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))))
890.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
883.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
765.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))

Compiler

Compiled 11351 to 9011 computations (20.6% saved)

simplify105.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5252	8858

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 l l) (sqrt.f64 2))
0.2b	(.f64 (.f64 x (*.f64 t t)) (sqrt.f64 1/2))
0.0b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 2) (.f64 x (sqrt.f64 1/2)))) (.f64 1/4 (/.f64 (.f64 (.f64 l l) (sqrt.f64 2)) (.f64 (.f64 x (*.f64 t t)) (sqrt.f64 1/2))))))
0.0b	(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 2) (.f64 x (sqrt.f64 1/2)))) (.f64 1/4 (/.f64 (.f64 (.f64 l l) (sqrt.f64 2)) (.f64 (.f64 x (.f64 t t)) (sqrt.f64 1/2)))))
0.5b	(/.f64 (sqrt.f64 2) (*.f64 x (sqrt.f64 1/2)))
1.0b	(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
5.9b	(.f64 x (.f64 t t))
15.7b	(/.f64 (.f64 (.f64 l l) (sqrt.f64 2)) (.f64 (.f64 x (*.f64 t t)) (sqrt.f64 1/2)))

rewrite55.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
35×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
22×	`add-sqr-sqrt_binary64_100`
16×	`sqrt-prod_binary64_94`
14×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
13×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
9×	`associate-l_binary64_19`
7×	`times-frac_binary64_84` `associate-r_binary64_18` `associate-/l*_binary64_23`
6×	`pow-prod-down_binary64_149`
5×	`unswap-sqr_binary64_46`
4×	`add-log-exp_binary64_117`
2×	`-commutative_binary64_9` `sqrt-pow1_binary64_96` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r_binary64_22` `clear-num_binary64_77` `pow1/2_binary64_158`
1×	`sqrt-unprod_binary64_98`

Counts

4 → 113

Calls

8 calls:

15.0ms	(/.f64 (.f64 (.f64 l l) (sqrt.f64 2)) (.f64 (.f64 x (*.f64 t t)) (sqrt.f64 1/2)))
7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
7.0ms	(/.f64 (sqrt.f64 2) (*.f64 x (sqrt.f64 1/2)))
6.0ms	(.f64 x (.f64 t t))
0.0ms	(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 2) (.f64 x (sqrt.f64 1/2)))) (.f64 1/4 (/.f64 (.f64 (.f64 l l) (sqrt.f64 2)) (.f64 (.f64 x (.f64 t t)) (sqrt.f64 1/2)))))

series502.0ms (0.3%)

Counts

4 → 18

Calls

4 calls:

363.0ms	(/.f64 (.f64 (.f64 l l) (sqrt.f64 2)) (.f64 (.f64 x (*.f64 t t)) (sqrt.f64 1/2)))
70.0ms	(.f64 x (.f64 t t))
69.0ms	(/.f64 (sqrt.f64 2) (*.f64 x (sqrt.f64 1/2)))
0.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))

Compiler

Compiled 1188 to 1128 computations (5.1% saved)

simplify90.0ms (0%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5003	2075

prune11.6s (6.1%)

Pruning

279 alts after pruning (273 fresh and 6 done)

	Pruned	Kept	Total
New	346	210	556
Fresh	13	63	76
Picked	0	0	0
Done	0	6	6
Total	359	279	638

Error

0.5b

Counts

638 → 279

Compiler

Compiled 29863 to 20242 computations (32.2% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))))
0.0b	(.f64 4 (/.f64 (.f64 t t) x))
0.0b	(.f64 2 (.f64 l (/.f64 l x)))
0.0b	(.f64 2 (.f64 t t))
0.6b	(+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x))))
2.5b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
9.5b	(/.f64 (*.f64 t t) x)
28.4b	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite49.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64_117`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-sqr-sqrt_binary64_100` `associate-*r/_binary64_20`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`flip-+_binary64_52` `pow1_binary64_139` `flip3-+_binary64_81`
4×	`frac-add_binary64_86` `sqrt-div_binary64_95` `sum-log_binary64_169`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129`
1×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `associate-+r+_binary64_10` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 64

Calls

8 calls:

14.0ms	(+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x))))
13.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
9.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.0ms	(/.f64 (*.f64 t t) x)
0.0ms	(.f64 2 (.f64 t t))

series1.2s (0.6%)

Counts

4 → 58

Calls

4 calls:

580.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
378.0ms	(+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x))))
148.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
70.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 3206 to 2776 computations (13.4% saved)

simplify70.0ms (0%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5006	4016

localize1.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (pow.f64 (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))) 1))))
0.0b	(.f64 4 (/.f64 (.f64 t t) x))
0.0b	(.f64 2 (/.f64 (.f64 l l) x))
0.0b	(.f64 2 (.f64 t t))
2.5b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
6.2b	(/.f64 (*.f64 l l) x)
9.5b	(/.f64 (*.f64 t t) x)
28.4b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (pow.f64 (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x))) 1)))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
3×	`sqrt-prod_binary64_94`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `sqrt-div_binary64_95` `clear-num_binary64_77` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158` `sum-log_binary64_169`

Counts

4 → 68

Calls

8 calls:

14.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (pow.f64 (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x))) 1)))
7.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.0ms	(/.f64 (*.f64 t t) x)
5.0ms	(/.f64 (*.f64 l l) x)
0.0ms	(.f64 2 (.f64 t t))

series883.0ms (0.5%)

Counts

4 → 46

Calls

4 calls:

592.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (pow.f64 (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x))) 1)))
145.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
75.0ms	(/.f64 (*.f64 t t) x)
71.0ms	(/.f64 (*.f64 l l) x)

Compiler

Compiled 2989 to 2541 computations (15% saved)

simplify74.0ms (0%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5055	3026

localize31.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))
0.0b	(/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))
0.0b	(sqrt.f64 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))
0.0b	(+.f64 (.f64 (/.f64 (.f64 t t) (.f64 (-.f64 x 1) l)) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1)))) (+.f64 (.f64 l (sqrt.f64 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (.f64 (/.f64 (.f64 t t) (.f64 (-.f64 x 1) l)) x))))
9.4b	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (.f64 (/.f64 (.f64 t t) (.f64 (-.f64 x 1) l)) x))
12.3b	(/.f64 (.f64 t t) (.f64 (-.f64 x 1) l))
12.3b	(/.f64 (.f64 t t) (.f64 (-.f64 x 1) l))
16.6b	(.f64 (/.f64 (.f64 t t) (*.f64 (-.f64 x 1) l)) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))))

rewrite218.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64_78`
71×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
69×	`sqrt-prod_binary64_94`
66×	`add-sqr-sqrt_binary64_100`
59×	`times-frac_binary64_84`
43×	`associate-l_binary64_19`
37×	`associate-r_binary64_18`
33×	`add-cube-cbrt_binary64_113`
32×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
18×	`distribute-lft-out--_binary64_30`
16×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
12×	`difference-of-squares_binary64_47` `distribute-lft-out_binary64_29`
11×	`div-inv_binary64_75` `pow1_binary64_139`
10×	`associate-*l/_binary64_21` `associate-/r/_binary64_24`
6×	`difference-of-sqr-1_binary64_48`
5×	`flip3--_binary64_82` `flip--_binary64_53`
4×	`add-log-exp_binary64_117` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `sqrt-div_binary64_95`
2×	`-commutative_binary64_9` `frac-2neg_binary64_89` `frac-times_binary64_88` `associate-/l_binary64_23` `associate-/r_binary64_22` `associate-r/_binary64_20` `clear-num_binary64_77`

Counts

4 → 177

Calls

8 calls:

78.0ms	(.f64 (/.f64 (.f64 t t) (*.f64 (-.f64 x 1) l)) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))))
77.0ms	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (.f64 (/.f64 (.f64 t t) (.f64 (-.f64 x 1) l)) x))
10.0ms	(/.f64 (.f64 t t) (.f64 (-.f64 x 1) l))
10.0ms	(/.f64 (.f64 t t) (.f64 (-.f64 x 1) l))
0.0ms	(+.f64 (.f64 (/.f64 (.f64 t t) (.f64 (-.f64 x 1) l)) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1)))) (+.f64 (.f64 l (sqrt.f64 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (.f64 (/.f64 (.f64 t t) (.f64 (-.f64 x 1) l)) x))))

series1.5s (0.8%)

Counts

4 → 38

Calls

4 calls:

579.0ms	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (.f64 (/.f64 (.f64 t t) (.f64 (-.f64 x 1) l)) x))
546.0ms	(.f64 (/.f64 (.f64 t t) (*.f64 (-.f64 x 1) l)) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))))
194.0ms	(/.f64 (.f64 t t) (.f64 (-.f64 x 1) l))
194.0ms	(/.f64 (.f64 t t) (.f64 (-.f64 x 1) l))

Compiler

Compiled 5770 to 4564 computations (20.9% saved)

simplify110.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4981	6845
1	4981	6845

localize7.0ms (0%)

Local error

Found 8 expressions with local error:

1.0b	(*.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (sqrt.f64 1/2)))
1.0b	(cbrt.f64 (sqrt.f64 1/2))
1.0b	(cbrt.f64 (sqrt.f64 1/2))
1.0b	(cbrt.f64 (sqrt.f64 1/2))
1.0b	(*.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (sqrt.f64 1/2)))
1.0b	(cbrt.f64 (sqrt.f64 1/2))
1.0b	(cbrt.f64 (sqrt.f64 1/2))
1.0b	(cbrt.f64 (sqrt.f64 1/2))

rewrite26.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`cbrt-prod_binary64_109`
44×	`add-sqr-sqrt_binary64_100`
29×	`sqrt-prod_binary64_94`
22×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`swap-sqr_binary64_45` `pow1_binary64_139`
9×	`associate-l_binary64_19` `pow1/3_binary64_160` `associate-r_binary64_18` `unswap-sqr_binary64_46`
6×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
2×	`pow-sqr_binary64_51` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-plus_binary64_141`

Counts

4 → 98

Calls

8 calls:

9.0ms	(*.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (sqrt.f64 1/2)))
2.0ms	(cbrt.f64 (sqrt.f64 1/2))
2.0ms	(cbrt.f64 (sqrt.f64 1/2))
2.0ms	(cbrt.f64 (sqrt.f64 1/2))
0.0ms	(cbrt.f64 (sqrt.f64 1/2))

series0.0ms (0%)

Counts

4 → 0

Calls

4 calls:

0.0ms	(cbrt.f64 (sqrt.f64 1/2))
0.0ms	(*.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (sqrt.f64 1/2)))
0.0ms	(cbrt.f64 (sqrt.f64 1/2))
0.0ms	(cbrt.f64 (sqrt.f64 1/2))

simplify69.0ms (0%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5137	1159

prune19.8s (10.4%)

Pruning

417 alts after pruning (408 fresh and 9 done)

	Pruned	Kept	Total
New	395	154	549
Fresh	14	254	268
Picked	0	0	0
Done	2	9	11
Total	411	417	828

Error

0.5b

Counts

828 → 417

Compiler

Compiled 38588 to 27784 computations (28% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (.f64 (*.f64 t t) (+.f64 2 (/.f64 4 x))))))
0.0b	(.f64 (.f64 t t) (+.f64 2 (/.f64 4 x)))
0.0b	(.f64 2 (.f64 l (/.f64 l x)))
0.0b	(+.f64 2 (/.f64 4 x))
0.2b	(*.f64 l (/.f64 l x))
0.4b	(*.f64 (sqrt.f64 2) t)
0.6b	(+.f64 (.f64 2 (.f64 l (/.f64 l x))) (.f64 (.f64 t t) (+.f64 2 (/.f64 4 x))))
28.4b	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (.f64 (.f64 t t) (+.f64 2 (/.f64 4 x)))))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_100`
16×	`add-cube-cbrt_binary64_113` `associate-r_binary64_18` `*-un-lft-identity_binary64_78`
13×	`associate-*r/_binary64_20`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`times-frac_binary64_84`
9×	`associate-l_binary64_19` `pow1_binary64_139`
7×	`sqrt-prod_binary64_94`
6×	`add-log-exp_binary64_117`
4×	`frac-add_binary64_86` `flip-+_binary64_52` `unswap-sqr_binary64_46` `sqrt-div_binary64_95` `flip3-+_binary64_81`
3×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
2×	`*-commutative_binary64_9` `associate-+r+_binary64_10` `pow-prod-down_binary64_149`
1×	`+-commutative_binary64_8` `distribute-lft-in_binary64_27` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `div-inv_binary64_75` `pow1/2_binary64_158` `sum-log_binary64_169`

Counts

4 → 86

Calls

8 calls:

10.0ms	(+.f64 (.f64 2 (.f64 l (/.f64 l x))) (.f64 (.f64 t t) (+.f64 2 (/.f64 4 x))))
9.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (.f64 (.f64 t t) (+.f64 2 (/.f64 4 x)))))
7.0ms	(*.f64 l (/.f64 l x))
5.0ms	(*.f64 (sqrt.f64 2) t)
0.0ms	(+.f64 2 (/.f64 4 x))

series1.1s (0.6%)

Counts

4 → 52

Calls

4 calls:

576.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (.f64 (.f64 t t) (+.f64 2 (/.f64 4 x)))))
412.0ms	(+.f64 (.f64 2 (.f64 l (/.f64 l x))) (.f64 (.f64 t t) (+.f64 2 (/.f64 4 x))))
70.0ms	(*.f64 l (/.f64 l x))
36.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 2925 to 2544 computations (13% saved)

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4975	3532
1	4975	3532

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 l (/.f64 l x))
0.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (exp.f64 (log.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (.f64 t t))))))))
0.0b	(.f64 4 (/.f64 (.f64 t t) x))
0.0b	(.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t)))
3.1b	(exp.f64 (log.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t))))))
9.5b	(/.f64 (*.f64 t t) x)
28.4b	(sqrt.f64 (exp.f64 (log.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t)))))))
29.5b	(log.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t)))))

rewrite51.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_100`
12×	`add-cube-cbrt_binary64_113` `log-div_binary64_165` `associate-r/_binary64_20` `-un-lft-identity_binary64_78`
10×	`log-prod_binary64_164` `add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114`
8×	`exp-diff_binary64_126` `exp-prod_binary64_130` `pow1_binary64_139`
7×	`exp-sum_binary64_124`
6×	`sqrt-prod_binary64_94` `frac-add_binary64_86` `flip-+_binary64_52` `flip3-+_binary64_81`
5×	`sqrt-pow1_binary64_96`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`times-frac_binary64_84` `associate-/r*_binary64_22` `log-pow_binary64_167`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91`
1×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-exp-log_binary64_118` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `rem-log-exp_binary64_119` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 81

Calls

8 calls:

12.0ms	(exp.f64 (log.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t))))))
11.0ms	(sqrt.f64 (exp.f64 (log.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t)))))))
10.0ms	(log.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t)))))
6.0ms	(/.f64 (*.f64 t t) x)
0.0ms	(.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t)))

series3.3s (1.7%)

Counts

4 → 68

Calls

4 calls:

1.6s	(exp.f64 (log.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t))))))
1.1s	(sqrt.f64 (exp.f64 (log.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t)))))))
479.0ms	(log.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t)))))
74.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 5423 to 4701 computations (13.3% saved)

simplify103.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4958	5254
1	4958	5254

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (.f64 (/.f64 t (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x))))))))
0.0b	(.f64 4 (.f64 (/.f64 t (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x))))
0.0b	(.f64 2 (/.f64 (.f64 l l) x))
0.0b	(.f64 2 (.f64 t t))
0.6b	(+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (.f64 (/.f64 t (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x))))))
2.5b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (.f64 (/.f64 t (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))))
6.2b	(/.f64 (*.f64 l l) x)
28.4b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (.f64 (/.f64 t (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))))))

rewrite53.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64_117`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`flip-+_binary64_52` `pow1_binary64_139` `flip3-+_binary64_81`
4×	`frac-add_binary64_86` `sqrt-div_binary64_95` `associate-*r/_binary64_20` `sum-log_binary64_169`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129`
1×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `associate-+r+_binary64_10` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 64

Calls

8 calls:

15.0ms	(+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (.f64 (/.f64 t (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x))))))
14.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (.f64 (/.f64 t (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))))))
9.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (.f64 (/.f64 t (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))))
5.0ms	(/.f64 (*.f64 l l) x)
0.0ms	(.f64 2 (.f64 t t))

series1.4s (0.7%)

Counts

4 → 58

Calls

4 calls:

639.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (.f64 (/.f64 t (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))))))
458.0ms	(+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (.f64 (/.f64 t (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x))))))
189.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (.f64 (/.f64 t (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))))
74.0ms	(/.f64 (*.f64 l l) x)

Compiler

Compiled 3360 to 2882 computations (14.2% saved)

simplify84.0ms (0%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5606	4843

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 4 (/.f64 (.f64 t t) x))
0.0b	(.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))
0.0b	(.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))
0.0b	(.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))
9.5b	(/.f64 (*.f64 t t) x)
28.4b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))
28.4b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))
28.4b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_100` `sqrt-div_binary64_95` `associate-*r/_binary64_20`
9×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `*-un-lft-identity_binary64_78`
7×	`pow1_binary64_139`
6×	`frac-add_binary64_86` `flip-+_binary64_52` `flip3-+_binary64_81`
4×	`add-log-exp_binary64_117`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `times-frac_binary64_84` `associate-/r*_binary64_22` `pow1/2_binary64_158`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
1×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77`

Counts

4 → 72

Calls

8 calls:

12.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))
5.0ms	(/.f64 (*.f64 t t) x)
0.0ms	(.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))

series1.9s (1%)

Counts

4 → 75

Calls

4 calls:

614.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))
605.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))
595.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))
91.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 10836 to 7443 computations (31.3% saved)

simplify108.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4962	5634
1	4962	5634

prune29.2s (15.4%)

Pruning

622 alts after pruning (609 fresh and 13 done)

	Pruned	Kept	Total
New	334	222	556
Fresh	16	387	403
Picked	0	0	0
Done	1	13	14
Total	351	622	973

Error

0.5b

Counts

973 → 622

Compiler

Compiled 20106 to 9558 computations (52.5% saved)

simplify1.2s (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5008	85752

regimes43.4s (22.8%)

Compiler: Compiled 356949 to 253029 computations (29.1% saved)

bsearch463.0ms (0.2%)

Steps

Iters	Range		Point
12	2528.410003700972	3.5418346604518734e+54	3.478259665751439e+54
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
9	3.085783124574877e-273	4.263824887753483e-266	4.192030017014753e-266
9	-5.34869388200843e+60	-1.9592891936126582e+55	-5.2919924128564495e+60

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes24.4s (12.8%)

Compiler: Compiled 185552 to 137327 computations (26% saved)

bsearch420.0ms (0.2%)

Steps

Iters	Range		Point
12	2528.410003700972	3.5418346604518734e+54	3.478259665751439e+54
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
9	3.085783124574877e-273	4.263824887753483e-266	4.192030017014753e-266
9	-5.34869388200843e+60	-1.9592891936126582e+55	-5.2919924128564495e+60

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes12.2s (6.4%)

Compiler: Compiled 108157 to 81550 computations (24.6% saved)

bsearch376.0ms (0.2%)

Steps

Iters	Range		Point
12	2528.410003700972	3.5418346604518734e+54	3.478259665751439e+54
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
9	3.085783124574877e-273	4.263824887753483e-266	4.192030017014753e-266
9	-5.34869388200843e+60	-1.9592891936126582e+55	-5.2919924128564495e+60

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes3.8s (2%)

Compiler: Compiled 33062 to 25904 computations (21.7% saved)

bsearch359.0ms (0.2%)

Steps

Iters	Range		Point
12	2528.410003700972	3.5418346604518734e+54	2.2544254585346644e+54
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
10	8.771738778533627e-241	5.306828555288177e-231	5.224886030954151e-231
9	-5.34869388200843e+60	-1.9592891936126582e+55	-5.2919924128564495e+60

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.5s (0.8%)

Compiler: Compiled 11175 to 9494 computations (15% saved)

bsearch399.0ms (0.2%)

Steps

Iters	Range		Point
12	2528.410003700972	3.5418346604518734e+54	3.478259665751439e+54
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
10	8.771738778533627e-241	5.306828555288177e-231	5.224886030954151e-231
9	-5.34869388200843e+60	-1.9592891936126582e+55	-5.2919924128564495e+60

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes890.0ms (0.5%)

Compiler: Compiled 3152 to 2945 computations (6.6% saved)

bsearch378.0ms (0.2%)

Steps

Iters	Range		Point
12	2528.410003700972	3.5418346604518734e+54	3.478259665751439e+54
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
10	8.771738778533627e-241	5.306828555288177e-231	5.224886030954151e-231
9	-5.34869388200843e+60	-1.9592891936126582e+55	-5.2919924128564495e+60

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes552.0ms (0.3%)

Compiler: Compiled 2609 to 2470 computations (5.3% saved)

bsearch352.0ms (0.2%)

Steps

Iters	Range		Point
12	2528.410003700972	3.5418346604518734e+54	3.478259665751439e+54
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
10	8.771738778533627e-241	5.306828555288177e-231	5.224886030954151e-231
7	-1.1283852598074376e+95	-4.974718574817269e+92	-1.108092975063467e+95

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes473.0ms (0.2%)

Compiler: Compiled 2126 to 2051 computations (3.5% saved)

bsearch337.0ms (0.2%)

Steps

Iters	Range		Point
12	2528.410003700972	3.5418346604518734e+54	3.3511096763505706e+54
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
10	8.771738778533627e-241	5.306828555288177e-231	5.224886030954151e-231
7	-1.1283852598074376e+95	-4.974718574817269e+92	-1.108092975063467e+95

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes432.0ms (0.2%)

Compiler: Compiled 1850 to 1817 computations (1.8% saved)

bsearch354.0ms (0.2%)

Steps

Iters	Range		Point
12	2528.410003700972	3.5418346604518734e+54	1.3403225210506321e+28
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
10	8.771738778533627e-241	5.306828555288177e-231	5.224886030954151e-231
5	-8.541927102298003e+43	-2.2854986777590336e+43	-7.88324907210378e+43

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes527.0ms (0.3%)

Compiler: Compiled 1470 to 1502 computations (-2.2% saved)

bsearch402.0ms (0.2%)

Steps

Iters	Range		Point
8	4.368337209777225e-98	1.890669391996735e-94	1.86238128998016e-94
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
10	8.771738778533627e-241	5.306828555288177e-231	5.224886030954151e-231
8	-4.91080953048334e-173	-4.569079206204532e-177	-4.826401648043764e-173

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes455.0ms (0.2%)

Compiler: Compiled 1285 to 1337 computations (-4% saved)

bsearch374.0ms (0.2%)

Steps

Iters	Range		Point
8	4.368337209777225e-98	1.890669391996735e-94	1.86238128998016e-94
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
10	8.771738778533627e-241	5.306828555288177e-231	5.224886030954151e-231
8	-4.91080953048334e-173	-4.569079206204532e-177	-4.826401648043764e-173

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes375.0ms (0.2%)

Compiler: Compiled 885 to 972 computations (-9.8% saved)

bsearch399.0ms (0.2%)

Steps

Iters	Range		Point
8	4.368337209777225e-98	1.890669391996735e-94	2.8307532102252626e-96
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
10	8.771738778533627e-241	5.306828555288177e-231	5.224886030954151e-231
8	-4.91080953048334e-173	-4.569079206204532e-177	-4.826401648043764e-173

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes316.0ms (0.2%)

Compiler: Compiled 590 to 707 computations (-19.8% saved)

bsearch381.0ms (0.2%)

Steps

Iters	Range		Point
8	4.368337209777225e-98	1.890669391996735e-94	1.86238128998016e-94
4	6.953583173136826e-185	1.1046888649798898e-184	7.081498969282516e-185
10	8.771738778533627e-241	5.306828555288177e-231	5.224886030954151e-231
8	-4.91080953048334e-173	-4.569079206204532e-177	-4.826401648043764e-173

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes209.0ms (0.1%)

Compiler: Compiled 324 to 426 computations (-31.5% saved)

bsearch221.0ms (0.1%)

Steps

Iters	Range		Point
9	-1.4614000194027568e-307	4.642652319568595e-304	4.57531098855737e-304
8	-4.91080953048334e-173	-4.569079206204532e-177	-4.826401648043764e-173

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes201.0ms (0.1%)

Compiler: Compiled 272 to 374 computations (-37.5% saved)

bsearch222.0ms (0.1%)

Steps

Iters	Range		Point
9	-1.4614000194027568e-307	4.642652319568595e-304	4.57531098855737e-304
8	-4.91080953048334e-173	-4.569079206204532e-177	-4.826401648043764e-173

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes31.0ms (0%)

Compiler: Compiled 12 to 42 computations (-250% saved)

bsearch167.0ms (0.1%)

Steps

Iters	Range		Point
9	-1.4614000194027568e-307	4.642652319568595e-304	4.57531098855737e-304

Compiler

Compiled 1325 to 1010 computations (23.8% saved)

simplify24.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	245	2017
1	245	2017

end0.0ms (0%)

sample7.4s (3.9%)

Algorithm

1×

intervals

Results

378.0ms	5281×	body	128	valid
327.0ms	1190×	body	1024	valid
219.0ms	829×	body	1024	nan
185.0ms	900×	body	512	valid
101.0ms	1489×	body	128	nan
99.0ms	514×	body	512	nan
76.0ms	561×	body	256	valid
41.0ms	304×	body	256	nan
23.0ms	68×	body	2048	valid

Compiler

Compiled 56462 to 40079 computations (29% saved)