Details

analyze265.0ms

Algorithm

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample36.0ms

Algorithm

intervals

Results

13.0ms	138×	body	160	valid
8.0ms	275×	pre	80	true
6.0ms	118×	body	80	valid
1.0ms	19×	body	80	nan

simplify111.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	928	24
1	928	24

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 26.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
26.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

series1.2s

Counts

4 → 12

Calls

4 calls:

257.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
222.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
432.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
277.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	786	92
1	786	92
0	786	92
1	786	92
0	22	11
1	22	11
0	1014	76
1	1014	76
0	1014	76
1	1014	76
0	1	3
1	1	3
0	676	357
1	676	357
0	676	357
1	676	357
0	1	3
1	1	3
0	728	764
1	728	764
0	728	764
1	728	764
0	22	11
1	22	11

simplify124.0ms

Counts

86 → 86

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4990	1919
1	4990	1919

prune120.0ms

Filtered

64 candidates to 86 candidates (-34.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	64	22	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	22	87

Merged error: 24.2b

Counts

87 → 22

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.4b	(/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
25.7b	(-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

70×	`times-frac_binary64`
58×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
26×	`associate-/l*_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
11×	`add-log-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64` `diff-log_binary64` `div-inv_binary64` `insert-posit16`
3×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `div-sub_binary64` `flip--_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`associate--l-_binary64` `associate--l+_binary64`

Counts

4 → 136

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
21.0ms	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
18.0ms	(/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
9.0ms	(-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b))

series2.5s

Counts

4 → 12

Calls

4 calls:

225.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.2s	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
820.0ms	(/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
246.0ms	(-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	711	487
1	711	487
0	711	487
1	711	487
0	1	3
1	1	3
0	2699	84
1	2699	84
0	2699	84
1	2699	84
0	1	3
1	1	3
0	3555	72
1	3555	72
0	3555	72
1	3555	72
0	1	3
1	1	3
0	676	357
1	676	357
0	676	357
1	676	357
0	1	3
1	1	3

simplify103.0ms

Counts

148 → 148

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4981	6865
1	4981	6865

prune301.0ms

Filtered

108 candidates to 148 candidates (-37.0%)

Pruning

38 alts after pruning (38 fresh and 0 done)

	Pruned	Kept	Total
New	126	22	148
Fresh	5	16	21
Picked	1	0	1
Done	0	0	0
Total	132	38	170

Merged error: 23.2b

Counts

170 → 38

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.3b	(.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) a) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
25.7b	(-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`associate-l_binary64`
11×	`add-log-exp_binary64`
7×	`distribute-lft-out_binary64`
6×	`pow1_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-/r*_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `insert-posit16`
3×	`sub-neg_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate--l-_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate--l+_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 121

Calls

4 calls:

6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
10.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
28.0ms	(.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) a) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
9.0ms	(-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b))

series1.9s

Counts

4 → 12

Calls

4 calls:

221.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
725.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
715.0ms	(.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) a) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
248.0ms	(-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	711	487
1	711	487
0	711	487
1	711	487
0	1	3
1	1	3
0	2306	197
1	2306	197
0	2306	197
1	2306	197
0	1	3
1	1	3
0	2369	161
1	2369	161
0	2369	161
1	2369	161
0	1	3
1	1	3
0	676	357
1	676	357
0	676	357
1	676	357
0	1	3
1	1	3

simplify116.0ms

Counts

133 → 133

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5021	4594

prune256.0ms

Filtered

98 candidates to 133 candidates (-35.7%)

Pruning

43 alts after pruning (43 fresh and 0 done)

	Pruned	Kept	Total
New	121	12	133
Fresh	6	31	37
Picked	1	0	1
Done	0	0	0
Total	128	43	171

Merged error: 23.2b

Counts

171 → 43

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) 3))
0.7b	(pow.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) 3)
25.7b	(-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

94×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
74×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
50×	`cbrt-prod_binary64`
44×	`unpow-prod-down_binary64` `cube-prod_binary64`
22×	`difference-of-squares_binary64`
21×	`distribute-lft-out_binary64`
10×	`associate-/r/_binary64`
9×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`associate-/r_binary64` `associate-/l_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `associate--l-_binary64` `pow1/3_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate--l+_binary64`

Counts

4 → 184

Calls

4 calls:

20.0ms	(/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
19.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) 3))
18.0ms	(pow.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) 3)
9.0ms	(-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b))

series2.1s

Counts

4 → 12

Calls

4 calls:

819.0ms	(/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
122.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) 3))
902.0ms	(pow.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) 3)
247.0ms	(-.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (.f64 b b))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	711	487
1	711	487
0	711	487
1	711	487
0	1	3
1	1	3
0	2814	163
1	2814	163
0	2814	163
1	2814	163
0	1	3
1	1	3
0	291	1798
1	291	1798
0	291	1798
1	291	1798
0	1	3
1	1	3
0	2699	84
1	2699	84
0	2699	84
1	2699	84
0	1	3
1	1	3

simplify163.0ms

Counts

196 → 196

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4982	10871
1	4982	10871

prune215.0ms

Filtered

102 candidates to 196 candidates (-92.2%)

Pruning

50 alts after pruning (49 fresh and 1 done)

	Pruned	Kept	Total
New	188	8	196
Fresh	1	41	42
Picked	0	1	1
Done	0	0	0
Total	189	50	239

Merged error: 23.2b

Counts

239 → 50

regimes452.0ms

Accuracy

0% (2.6b remaining)

Error of 27.3b against oracle of 24.7b and baseline of 27.3b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	81	50
1	81	50

end0.0ms

sample1.1s

Algorithm

intervals

Results

425.0ms	4437×	body	160	valid
249.0ms	8860×	pre	80	true
180.0ms	3563×	body	80	valid
47.0ms	860×	body	80	nan

Details

analyze265.0ms

sample36.0ms

simplify111.0ms

prune6.0ms

localize11.0ms

rewrite37.0ms

series1.2s

simplify124.0ms

prune120.0ms

localize14.0ms

rewrite60.0ms

series2.5s

simplify103.0ms

prune301.0ms

localize13.0ms

rewrite58.0ms

series1.9s

simplify116.0ms

prune256.0ms

localize16.0ms

rewrite77.0ms

series2.1s

simplify163.0ms

prune215.0ms

regimes452.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample1.1s

Profiling