Details

analyze1.1s (5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5644	164
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
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)

sample69.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	173×	body	128	valid
8.0ms	28×	body	1024	valid
8.0ms	27×	body	1024	nan
7.0ms	31×	body	512	valid
5.0ms	64×	body	128	nan
3.0ms	14×	body	512	nan
3.0ms	19×	body	256	valid
2.0ms	5×	body	2048	valid
1.0ms	10×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5192	41

prune3.0ms (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

40.9b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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))))
0.5b	(*.f64 (sqrt.f64 2) t)
13.6b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
20.1b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite255.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

40.7b

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

Counts

4 → 80

Calls

4 calls:

24.0ms	(/.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))))
19.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
18.0ms	(-.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)

Compiler

Compiled 3564 to 2030 computations (43% saved)

series4.8s (22.3%)

Error

6.5b

Counts

4 → 60

Calls

4 calls:

2.3s	(/.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))))
1.5s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
832.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
32.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 10944 to 9103 computations (16.8% saved)

simplify123.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4980	6556
1	4980	6556

prune316.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	131	9	140
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Error

6.5b

Counts

141 → 9

Compiler

Compiled 6121 to 3805 computations (37.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.6b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
4.3b	(/.f64 (*.f64 l l) x)
7.8b	(/.f64 (*.f64 t t) x)
28.6b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite168.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

14×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
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×	`sqrt-div_binary64_95` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `sqrt-prod_binary64_94`
2×	`associate-r/_binary64_20` `frac-add_binary64_86` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `sum-log_binary64_169` `+-commutative_binary64_8`

Counts

4 → 70

Calls

4 calls:

12.0ms	(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)))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 2731 to 1340 computations (50.9% saved)

series924.0ms (4.3%)

Error

0.2b

Counts

4 → 43

Calls

4 calls:

542.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
139.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
97.0ms	(/.f64 (*.f64 t t) x)
78.0ms	(/.f64 (*.f64 l l) x)

Compiler

Compiled 4155 to 3358 computations (19.2% saved)

simplify90.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5037	2638

prune243.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	112	10	122

Error

0.2b

Counts

122 → 10

Compiler

Compiled 3936 to 2186 computations (44.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))
3.6b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
7.8b	(/.f64 (*.f64 t t) x)
28.6b	(sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x)))))

rewrite273.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

16×	`associate-*r/_binary64_20`
12×	`frac-add_binary64_86`
11×	`add-log-exp_binary64_117`
9×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `flip3-+_binary64_81` `flip-+_binary64_52`
8×	`add-sqr-sqrt_binary64_100` `sqrt-div_binary64_95`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`pow1_binary64_139`
4×	`frac-times_binary64_88` `associate-*l/_binary64_21` `sum-log_binary64_169`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`div-exp_binary64_129` `cbrt-undiv_binary64_112` `+-commutative_binary64_8`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l*_binary64_23` `associate-+r+_binary64_10`

Counts

4 → 72

Calls

4 calls:

28.0ms	(+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))
28.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x)))))
13.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
9.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 4308 to 1743 computations (59.5% saved)

series1.5s (6.9%)

Error

0.2b

Counts

4 → 55

Calls

4 calls:

634.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x)))))
467.0ms	(+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))
190.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
81.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 5043 to 4038 computations (19.9% saved)

simplify75.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5006	4404

prune300.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	127	10	137

Error

0.2b

Counts

137 → 10

Compiler

Compiled 5158 to 2621 computations (49.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.3b	(/.f64 (*.f64 l l) x)
7.8b	(/.f64 (*.f64 t t) x)
28.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))
37.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))) 3))

rewrite224.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

18×	`cbrt-prod_binary64_109`
15×	`add-sqr-sqrt_binary64_100`
14×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`sqrt-prod_binary64_94`
8×	`associate-*r/_binary64_20` `sqrt-div_binary64_95`
6×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106` `times-frac_binary64_84` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117` `flip3-+_binary64_81` `frac-add_binary64_86` `cube-div_binary64_107` `cbrt-div_binary64_110` `flip-+_binary64_52` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
2×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l*_binary64_23`
1×	`pow1/3_binary64_160` `unpow3_binary64_144` `cube-mult_binary64_108` `sqr-pow_binary64_50` `rem-cbrt-cube_binary64_102` `pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91`

Counts

4 → 90

Calls

4 calls:

11.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))) 3))
10.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(/.f64 (*.f64 l l) x)
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))

Compiler

Compiled 3993 to 1804 computations (54.8% saved)

series1.4s (6.6%)

Error

0.2b

Counts

4 → 54

Calls

4 calls:

599.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))) 3))
543.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))
111.0ms	(/.f64 (*.f64 t t) x)
82.0ms	(/.f64 (*.f64 l l) x)

Compiler

Compiled 5922 to 4894 computations (17.4% saved)

simplify103.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4973	4460
1	4973	4460

prune247.0ms (1.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	144	10	154

Error

0.2b

Counts

154 → 10

Compiler

Compiled 5068 to 2631 computations (48.1% saved)

regimes3.1s (14.4%)

Accuracy

Total 8.7b remaining (95.5%)

Threshold costs 0b (0%)

Compiler

Compiled 27911 to 20117 computations (27.9% saved)

bsearch598.0ms (2.8%)

Steps

Iters	Range		Point
7	1.7842973147487176e+125	3.696547172273562e+126	2.2674113060888642e+126
7	3.3356905738861366e-144	1.0553037257106848e-142	3.385594735519463e-144
9	-6.151127738508492e-306	1.6955969546352727e-305	1.673826578300523e-305
9	-4.300770839754357e-236	-3.335035429371588e-242	-4.222777320075483e-236
5	-3.9698173632769544e-154	-1.554419332801898e-154	-1.5844530436624705e-154
6	-1.2670470703380613e-41	-1.111822514133303e-42	-1.2351728058409963e-41

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	251	302
1	251	302

end0.0ms (0%)

sample5.5s (25.5%)

Algorithm

1×

intervals

Results

450.0ms	5338×	body	128	valid
357.0ms	1103×	body	1024	valid
268.0ms	851×	body	1024	nan
239.0ms	949×	body	512	valid
121.0ms	527×	body	512	nan
120.0ms	1508×	body	128	nan
88.0ms	530×	body	256	valid
49.0ms	310×	body	256	nan
31.0ms	80×	body	2048	valid

Compiler

Compiled 4098 to 2967 computations (27.6% saved)

Details

analyze1.1s (5%)

sample69.0ms (0.3%)

simplify81.0ms (0.4%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite255.0ms (1.2%)

series4.8s (22.3%)

simplify123.0ms (0.6%)

prune316.0ms (1.5%)

localize19.0ms (0.1%)

rewrite168.0ms (0.8%)

series924.0ms (4.3%)

simplify90.0ms (0.4%)

prune243.0ms (1.1%)

localize23.0ms (0.1%)

rewrite273.0ms (1.3%)

series1.5s (6.9%)

simplify75.0ms (0.3%)

prune300.0ms (1.4%)

localize18.0ms (0.1%)

rewrite224.0ms (1%)

series1.4s (6.6%)

simplify103.0ms (0.5%)

prune247.0ms (1.1%)

regimes3.1s (14.4%)

bsearch598.0ms (2.8%)

simplify8.0ms (0%)

end0.0ms (0%)

sample5.5s (25.5%)

Profiling