Details

analyze958.0ms (3.8%)

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)

sample58.0ms (0.2%)

Algorithm

1×

intervals

Results

12.0ms	179×	body	128	valid
9.0ms	35×	body	1024	valid
6.0ms	28×	body	512	valid
6.0ms	22×	body	1024	nan
3.0ms	51×	body	128	nan
3.0ms	14×	body	512	nan
2.0ms	12×	body	256	valid
1.0ms	7×	body	256	nan
1.0ms	2×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

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

42.0b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize19.0ms (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)
14.7b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
20.8b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite223.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

41.9b

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:

19.0ms	(/.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))))
15.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
15.0ms	(sqrt.f64 (-.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)

series3.2s (12.8%)

Error

5.5b

Counts

4 → 61

Calls

4 calls:

1.3s	(/.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))))
797.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
685.0ms	(-.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 10316 to 8605 computations (16.6% saved)

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5043	7786

prune348.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	6	142

Error

5.5b

Counts

142 → 6

Compiler

Compiled 6908 to 4338 computations (37.2% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

15.2b	(/.f64 (*.f64 l l) (pow.f64 x 3))
20.7b	(/.f64 (*.f64 t t) (pow.f64 x 3))
20.9b	(/.f64 (.f64 t t) (.f64 x x))
26.8b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x)))))))))

rewrite547.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

Rules

42×	`add-exp-log_binary64_116` `associate-*r/_binary64_20`
38×	`frac-add_binary64_86`
26×	`add-cbrt-cube_binary64_114`
25×	`times-frac_binary64_84` `associate-/r*_binary64_22`
18×	`add-sqr-sqrt_binary64_100`
17×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
16×	`div-exp_binary64_129`
14×	`sqrt-div_binary64_95`
12×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
10×	`prod-exp_binary64_127`
9×	`flip3-+_binary64_81` `flip-+_binary64_52`
8×	`cbrt-undiv_binary64_112`
6×	`cbrt-unprod_binary64_111`
5×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow3_binary64_144` `cube-mult_binary64_108` `sqr-pow_binary64_50`
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 → 134

Calls

4 calls:

33.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x)))))))))
7.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
7.0ms	(/.f64 (.f64 t t) (.f64 x x))
7.0ms	(/.f64 (*.f64 l l) (pow.f64 x 3))

Compiler

Compiled 13138 to 5192 computations (60.5% saved)

series1.6s (6.2%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

1.1s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x)))))))))
122.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
113.0ms	(/.f64 (*.f64 l l) (pow.f64 x 3))
103.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 10113 to 7570 computations (25.1% saved)

simplify99.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5058	9987

prune646.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	170	9	179

Error

0.1b

Counts

179 → 9

Compiler

Compiled 14798 to 6488 computations (56.2% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

20.9b	(/.f64 (.f64 t t) (.f64 x x))
20.9b	(/.f64 (.f64 t t) (.f64 x x))
27.6b	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))
27.6b	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))

rewrite900.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

108×	`associate-*r/_binary64_20`
104×	`frac-add_binary64_86`
36×	`cbrt-div_binary64_110`
28×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
26×	`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 → 100

Calls

4 calls:

35.0ms	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))
33.0ms	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))
7.0ms	(/.f64 (.f64 t t) (.f64 x x))
7.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 22200 to 7774 computations (65% saved)

series5.0s (19.8%)

Error

0.1b

Counts

4 → 52

Calls

4 calls:

2.2s	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))
2.2s	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))
123.0ms	(/.f64 (.f64 t t) (.f64 x x))
108.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 22976 to 15956 computations (30.6% saved)

simplify175.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5195	21324

prune1.3s (5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	151	10	161

Error

0.1b

Counts

161 → 10

Compiler

Compiled 27513 to 11551 computations (58% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
0.0b	(+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))
0.4b	(.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))
0.5b	(*.f64 (sqrt.f64 2) t)

rewrite204.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

20×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
18×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113` `-un-lft-identity_binary64_78` `associate-r*_binary64_18`
9×	`sqrt-prod_binary64_94` `associate-l_binary64_19` `associate-*r/_binary64_20`
8×	`pow1_binary64_139`
6×	`prod-exp_binary64_127` `add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `sqrt-div_binary64_95`
4×	`unswap-sqr_binary64_46` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
3×	`frac-add_binary64_86` `flip3-+_binary64_81` `flip-+_binary64_52` `div-inv_binary64_75` `associate-/r/_binary64_24`
2×	`pow-prod-down_binary64_149` `*-commutative_binary64_9` `distribute-lft-out_binary64_29`
1×	`sum-log_binary64_169` `+-commutative_binary64_8` `frac-2neg_binary64_89` `times-frac_binary64_84` `clear-num_binary64_77` `associate-/l_binary64_23` `associate-/r_binary64_22`

Counts

4 → 85

Calls

4 calls:

17.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
15.0ms	(.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))
14.0ms	(+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))
5.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 2867 to 2213 computations (22.8% saved)

series603.0ms (2.4%)

Error

0.1b

Counts

4 → 37

Calls

4 calls:

271.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
211.0ms	(.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))
36.0ms	(+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))
35.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 2184 to 1986 computations (9.1% saved)

simplify74.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4983	2953
1	4983	2953

prune186.0ms (0.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	123	9	132

Error

0.1b

Counts

132 → 9

Compiler

Compiled 3243 to 2568 computations (20.8% saved)

regimes3.2s (12.6%)

Accuracy

Total 11.2b remaining (97.4%)

Threshold costs 0b (0%)

Compiler

Compiled 52107 to 29369 computations (43.6% saved)

bsearch137.0ms (0.5%)

Steps

Iters	Range		Point
8	1.0472652230968589e+91	2.2926702321004158e+95	1.8982460853244696e+94
6	-1.1070090908206272e+22	-1.673317679952176e+21	-9.342725470987389e+21

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	120
1	79	120

end0.0ms (0%)

sample5.6s (22.2%)

Algorithm

1×

intervals

Results

380.0ms	5303×	body	128	valid
306.0ms	1108×	body	1024	valid
225.0ms	847×	body	1024	nan
196.0ms	970×	body	512	valid
106.0ms	1587×	body	128	nan
102.0ms	494×	body	512	nan
76.0ms	545×	body	256	valid
39.0ms	281×	body	256	nan
26.0ms	74×	body	2048	valid

Compiler

Compiled 7501 to 4251 computations (43.3% saved)

Details

analyze958.0ms (3.8%)

sample58.0ms (0.2%)

simplify71.0ms (0.3%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite223.0ms (0.9%)

series3.2s (12.8%)

simplify80.0ms (0.3%)

prune348.0ms (1.4%)

localize32.0ms (0.1%)

rewrite547.0ms (2.2%)

series1.6s (6.2%)

simplify99.0ms (0.4%)

prune646.0ms (2.6%)

localize35.0ms (0.1%)

rewrite900.0ms (3.6%)

series5.0s (19.8%)

simplify175.0ms (0.7%)

prune1.3s (5%)

localize12.0ms (0%)

rewrite204.0ms (0.8%)

series603.0ms (2.4%)

simplify74.0ms (0.3%)

prune186.0ms (0.7%)

regimes3.2s (12.6%)

bsearch137.0ms (0.5%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.6s (22.2%)

Profiling