Details

analyze1.4s (3.2%)

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)

sample105.0ms (0.2%)

Algorithm

1×

intervals

Results

23.0ms	182×	body	128	valid
21.0ms	31×	body	1024	valid
10.0ms	21×	body	1024	nan
9.0ms	25×	body	512	valid
6.0ms	18×	body	512	nan
4.0ms	18×	body	256	valid
4.0ms	35×	body	128	nan
2.0ms	9×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify281.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	5192	41

prune7.0ms (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

41.5b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize35.0ms (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)
10.3b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.8b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite439.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

41.3b

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:

40.0ms	(/.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))))
37.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
30.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
11.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 3564 to 2030 computations (43% saved)

series7.5s (16.9%)

Error

2.9b

Counts

4 → 64

Calls

4 calls:

3.2s	(/.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))))
2.6s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
1.2s	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
61.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 12912 to 10756 computations (16.7% saved)

simplify178.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5246	8799

prune1.1s (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	138	6	144
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	138	7	145

Error

2.9b

Counts

145 → 7

Compiler

Compiled 7572 to 4849 computations (36% saved)

localize48.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.1b	(/.f64 (*.f64 t t) x)
13.6b	(/.f64 (.f64 l l) (.f64 x x))
18.3b	(/.f64 (.f64 t t) (.f64 x x))
25.2b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))

rewrite387.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

2.9b

Rules

33×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
20×	`associate-*r/_binary64_20`
16×	`frac-add_binary64_86`
10×	`sqrt-div_binary64_95` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
9×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111`
8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113` `flip3-+_binary64_81` `flip-+_binary64_52` `*-un-lft-identity_binary64_78`
5×	`pow1_binary64_139` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117`
3×	`sqrt-prod_binary64_94` `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`

Counts

4 → 86

Calls

4 calls:

39.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
14.0ms	(/.f64 (.f64 t t) (.f64 x x))
14.0ms	(/.f64 (.f64 l l) (.f64 x x))
10.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 5815 to 1665 computations (71.4% saved)

series2.7s (6.1%)

Error

0.1b

Counts

4 → 41

Calls

4 calls:

2.0s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
174.0ms	(/.f64 (.f64 t t) (.f64 x x))
167.0ms	(/.f64 (.f64 l l) (.f64 x x))
147.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 8042 to 6171 computations (23.3% saved)

simplify181.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4998	5402
1	4998	5402

prune462.0ms (1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	121	6	127
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	122	12	134

Error

0.1b

Counts

134 → 12

Compiler

Compiled 7606 to 3171 computations (58.3% saved)

localize55.0ms (0.1%)

Local error

Found 4 expressions with local error:

18.3b	(/.f64 (.f64 t t) (.f64 x x))
18.3b	(/.f64 (.f64 t t) (.f64 x x))
25.2b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
25.2b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))

rewrite707.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

40×	`associate-*r/_binary64_20`
32×	`frac-add_binary64_86`
28×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
20×	`sqrt-div_binary64_95`
14×	`flip3-+_binary64_81` `flip-+_binary64_52`
8×	`add-sqr-sqrt_binary64_100` `prod-exp_binary64_127` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `cbrt-unprod_binary64_111`
6×	`pow1_binary64_139` `add-cube-cbrt_binary64_113` `sqrt-prod_binary64_94` `*-un-lft-identity_binary64_78`
4×	`add-log-exp_binary64_117`
2×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `times-frac_binary64_84` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-/r_binary64_22`

Counts

4 → 88

Calls

4 calls:

43.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
40.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
14.0ms	(/.f64 (.f64 t t) (.f64 x x))
14.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 11120 to 2892 computations (74% saved)

series6.0s (13.5%)

Error

0.1b

Counts

4 → 60

Calls

4 calls:

2.5s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
2.4s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
203.0ms	(/.f64 (.f64 t t) (.f64 x x))
196.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 20624 to 14248 computations (30.9% saved)

simplify213.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4996	10356
1	4996	10356

prune1.0s (2.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	148	12	160

Error

0.1b

Counts

160 → 12

Compiler

Compiled 16249 to 6227 computations (61.7% saved)

localize59.0ms (0.1%)

Local error

Found 4 expressions with local error:

18.3b	(/.f64 (.f64 t t) (.f64 x x))
18.3b	(/.f64 (.f64 t t) (.f64 x x))
25.9b	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
25.9b	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))

rewrite623.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`associate-*r/_binary64_20`
32×	`frac-add_binary64_86`
28×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
20×	`cbrt-div_binary64_110`
14×	`flip3-+_binary64_81` `flip-+_binary64_52`
8×	`prod-exp_binary64_127` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `cbrt-unprod_binary64_111`
6×	`add-cube-cbrt_binary64_113` `cbrt-prod_binary64_109` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`pow1_binary64_139` `add-log-exp_binary64_117`
2×	`pow1/3_binary64_160` `frac-2neg_binary64_89` `times-frac_binary64_84` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-/r_binary64_22`

Counts

4 → 84

Calls

4 calls:

38.0ms	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
38.0ms	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
13.0ms	(/.f64 (.f64 t t) (.f64 x x))
13.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 10776 to 2784 computations (74.2% saved)

series4.8s (10.8%)

Error

0.1b

Counts

4 → 48

Calls

4 calls:

2.1s	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
2.1s	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
181.0ms	(/.f64 (.f64 t t) (.f64 x x))
166.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 14878 to 10009 computations (32.7% saved)

simplify269.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4945	8516
1	4945	8516

prune875.0ms (2%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	131	13	144

Error

0.0b

Counts

144 → 13

Compiler

Compiled 13750 to 4719 computations (65.7% saved)

regimes4.2s (9.5%)

Accuracy

Total 10.3b remaining (96.7%)

Threshold costs 0b (0%)

Compiler

Compiled 28346 to 19097 computations (32.6% saved)

bsearch885.0ms (2%)

Steps

Iters	Range		Point
8	5.124700046123233e+30	9.208728260002318e+34	3.425085433279833e+34
10	-4.62742340298622e-278	-3.06488474066442e-290	-4.571719205972361e-278
9	-4.95655488454908e-157	-3.7947010859515303e-165	-3.8518359656331984e-165
9	-17852040131584136.0	-28738150490.34724	-17682194664272242.0

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify15.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	275	286
1	275	286

end0.0ms (0%)

sample9.9s (22.3%)

Algorithm

1×

intervals

Results

761.0ms	5350×	body	128	valid
657.0ms	1159×	body	1024	valid
458.0ms	805×	body	1024	nan
364.0ms	870×	body	512	valid
222.0ms	556×	body	512	nan
202.0ms	1537×	body	128	nan
149.0ms	546×	body	256	valid
72.0ms	277×	body	256	nan
56.0ms	75×	body	2048	valid

Compiler

Compiled 4277 to 2906 computations (32.1% saved)

Details

analyze1.4s (3.2%)

sample105.0ms (0.2%)

simplify281.0ms (0.6%)

prune7.0ms (0%)

localize35.0ms (0.1%)

rewrite439.0ms (1%)

series7.5s (16.9%)

simplify178.0ms (0.4%)

prune1.1s (2.4%)

localize48.0ms (0.1%)

rewrite387.0ms (0.9%)

series2.7s (6.1%)

simplify181.0ms (0.4%)

prune462.0ms (1%)

localize55.0ms (0.1%)

rewrite707.0ms (1.6%)

series6.0s (13.5%)

simplify213.0ms (0.5%)

prune1.0s (2.3%)

localize59.0ms (0.1%)

rewrite623.0ms (1.4%)

series4.8s (10.8%)

simplify269.0ms (0.6%)

prune875.0ms (2%)

regimes4.2s (9.5%)

bsearch885.0ms (2%)

simplify15.0ms (0%)

end0.0ms (0%)

sample9.9s (22.3%)

Profiling