Details

analyze268.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample76.0ms

Algorithm

intervals

Results

37.0ms	74×	body	1280	valid
18.0ms	64×	body	640	valid
8.0ms	26×	body	2560	valid
3.0ms	21×	body	320	valid
2.0ms	55×	body	80	valid
2.0ms	16×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

prune1.0ms

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: 54.5b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.9b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.0b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
13.0b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 45

Calls

3 calls:

10.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
8.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series595.0ms

Counts

3 → 9

Calls

3 calls:

202.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
228.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
165.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	1208	9
1	1208	9
0	1208	9
1	1208	9
0	1	3
1	1	3
0	1076	9
1	1076	9
0	1076	9
1	1076	9
0	1	3
1	1	3

simplify120.0ms

Counts

54 → 54

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4974	733
1	4974	733

prune63.0ms

Filtered

39 candidates to 54 candidates (-38.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	46	8	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	8	55

Merged error: 44.5b

Counts

55 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
0.8b	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.0b	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
13.0b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
24×	`log-prod_binary64`
16×	`difference-of-squares_binary64`
11×	`sqrt-prod_binary64`
9×	`add-exp-log_binary64`
8×	`distribute-lft-out--_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r/_binary64` `insert-posit16`
3×	`flip3--_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64`

Counts

4 → 109

Calls

4 calls:

10.0ms	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
8.0ms	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
10.0ms	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

359.0ms	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
211.0ms	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
385.0ms	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
163.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	2829	9
1	2829	9
0	2829	9
1	2829	9
0	1	3
1	1	3
0	1102	9
1	1102	9
0	1102	9
1	1102	9
0	1	3
1	1	3
0	2761	9
1	2761	9
0	2761	9
1	2761	9
0	1	3
1	1	3

simplify172.0ms

Counts

121 → 121

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4930	2601
1	4930	2601

prune101.0ms

Filtered

81 candidates to 121 candidates (-49.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	119	10	129

Merged error: 42.2b

Counts

129 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.0b	(log.f64 (cbrt.f64 (/.f64 -1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) 3))))
8.5b	(cbrt.f64 (/.f64 -1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) 3)))
13.0b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

120×	`cbrt-prod_binary64`
115×	`add-sqr-sqrt_binary64`
108×	`times-frac_binary64`
88×	`*-un-lft-identity_binary64`
63×	`log-prod_binary64`
62×	`add-cube-cbrt_binary64`
36×	`unpow-prod-down_binary64` `cube-prod_binary64`
26×	`difference-of-squares_binary64`
16×	`sqrt-prod_binary64`
13×	`distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
5×	`add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `associate-/r/_binary64` `cube-div_binary64` `insert-posit16`
3×	`flip3--_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `pow1/3_binary64` `log-pow_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `rem-log-exp_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `log-div_binary64` `flip-+_binary64`

Counts

4 → 176

Calls

4 calls:

13.0ms	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
18.0ms	(log.f64 (cbrt.f64 (/.f64 -1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) 3))))
14.0ms	(cbrt.f64 (/.f64 -1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) 3)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series479.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
49.0ms	(log.f64 (cbrt.f64 (/.f64 -1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) 3))))
49.0ms	(cbrt.f64 (/.f64 -1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) 3)))
167.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	61	9
1	61	9
0	61	9
1	61	9
0	1	3
1	1	3
0	211	9
1	211	9
0	211	9
1	211	9
0	1	3
1	1	3
0	1102	9
1	1102	9
0	1102	9
1	1102	9
0	1	3
1	1	3

simplify127.0ms

Counts

188 → 188

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5356	6271

prune158.0ms

Filtered

102 candidates to 188 candidates (-84.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	187	11	198

Merged error: 42.1b

Counts

198 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

8.5b	(cbrt.f64 (/.f64 -1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) 3)))
13.0b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
13.0b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
13.0b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64`
60×	`cbrt-prod_binary64`
54×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
18×	`unpow-prod-down_binary64` `cube-prod_binary64`
15×	`sqrt-prod_binary64`
12×	`difference-of-squares_binary64`
7×	`pow1_binary64`
6×	`distribute-lft-out--_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`flip3-+_binary64` `pow1/2_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`associate-/r/_binary64` `cube-div_binary64`
1×	`cbrt-div_binary64` `flip3--_binary64` `pow1/3_binary64` `div-inv_binary64` `flip--_binary64`

Counts

4 → 118

Calls

4 calls:

14.0ms	(cbrt.f64 (/.f64 -1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) 3)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series549.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cbrt.f64 (/.f64 -1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) 3)))
169.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
166.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
170.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	61	9
1	61	9
0	61	9
1	61	9
0	1	3
1	1	3

simplify134.0ms

Counts

130 → 130

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	5332	3297

prune236.0ms

Filtered

78 candidates to 130 candidates (-66.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	130	11	141

Merged error: 42.1b

Counts

141 → 11

regimes79.0ms

Accuracy

99.5% (0.1b remaining)

Error of 40.2b against oracle of 40.2b and baseline of 52.9b

bsearch85.0ms

Steps

Iters	Range	Point
10	1.5604891464706173e+147	1.1136228946479473e+157	1.345072362821146e+154
9	-8.334418280474293e-08	-6.652663162433878e-14	-3.43856601333689e-08
9	-1.8260679316704666e+161	-1.0953075004062121e+152	-1.345236605992239e+154

Iters

Range

Point

1.5604891464706173e+147

1.1136228946479473e+157

1.345072362821146e+154

-8.334418280474293e-08

-6.652663162433878e-14

-3.43856601333689e-08

-1.8260679316704666e+161

-1.0953075004062121e+152

-1.345236605992239e+154

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	42	73
1	42	73

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2286×	body	1280	valid
445.0ms	1626×	body	640	valid
279.0ms	850×	body	2560	valid
137.0ms	805×	body	320	valid
85.0ms	2056×	body	80	valid
38.0ms	377×	body	160	valid

Iter	Nodes	Cost
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	61	9
1	61	9
0	61	9
1	61	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	61	9
1	61	9
0	61	9
1	61	9
0	1	3
1	1	3

Details

analyze268.0ms

sample76.0ms

simplify19.0ms

prune1.0ms

localize6.0ms

rewrite24.0ms

series595.0ms

simplify120.0ms

prune63.0ms

localize8.0ms

rewrite39.0ms

series1.1s

simplify172.0ms

prune101.0ms

localize10.0ms

rewrite63.0ms

series479.0ms

simplify127.0ms

prune158.0ms

localize19.0ms

rewrite39.0ms

series549.0ms

simplify134.0ms

prune236.0ms

regimes79.0ms

bsearch85.0ms

simplify7.0ms

end0.0ms

sample2.2s

Profiling

Iter	Nodes	Cost
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	788	9
1	788	9
0	788	9
1	788	9
0	1	3
1	1	3
0	61	9
1	61	9
0	61	9
1	61	9
0	1	3
1	1	3