Details

sample63.0ms

Algorithm

intervals

Results

12.0ms	176×	body	80	valid
9.0ms	33×	body	2560	valid
6.0ms	29×	body	1280	valid
4.0ms	76×	body	80	nan
3.0ms	16×	body	640	valid
3.0ms	8×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	5×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	12
1	29	12

prune22.0ms

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: 35.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

10.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5242	1411

prune158.0ms

Filtered

70 candidates to 96 candidates (-37.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	84	12	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 5.7b

Counts

97 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.5b	(/ (/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
10.0b	(/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
97×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
21×	`associate-/l*`
16×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`div-inv` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp`
3×	`flip3--` `div-sub` `distribute-frac-neg` `sqrt-prod` `flip--` `associate-/l/`
2×	`frac-2neg` `sub0-neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 156

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
10.0ms	(/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(/ (/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
57.0ms	(/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4884	3670
1	4884	3670

prune192.0ms

Filtered

130 candidates to 168 candidates (-29.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	171	9	180

Merged error: 5.5b

Counts

180 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
0.6b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out`
4×	`associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 72

Calls

4 calls:

10.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
6.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5054	1111

prune111.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	83	10	93

Merged error: 5.5b

Counts

93 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

14.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
6.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5159	3292

prune135.0ms

Filtered

101 candidates to 174 candidates (-72.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	174	10	184

Merged error: 5.5b

Counts

184 → 10

regimes321.0ms

Accuracy

94.6% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 29.5b

bsearch79.0ms

Steps

Iters	Range	Point
6	1.1487243557305423e+102	6.148420459531844e+102	3.9588277603203294e+102
7	-3.9639939611996993e-296	-1.2313747004456891e-297	-1.5056723658874731e-296
8	-8.704679048448932e+71	-1.0976727662850034e+68	-1.013848001599699e+70

Iters

Range

Point

1.1487243557305423e+102

6.148420459531844e+102

3.9588277603203294e+102

-3.9639939611996993e-296

-1.2313747004456891e-297

-1.5056723658874731e-296

-8.704679048448932e+71

-1.0976727662850034e+68

-1.013848001599699e+70

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	57
1	48	57

end0.0ms

sample1.5s

Algorithm

intervals

Results

296.0ms	1069×	body	2560	valid
280.0ms	5829×	body	80	valid
199.0ms	907×	body	1280	valid
133.0ms	2967×	body	80	nan
82.0ms	486×	body	640	valid
41.0ms	130×	body	5120	valid
26.0ms	200×	body	320	valid
9.0ms	101×	body	160	valid

Details

sample63.0ms

simplify9.0ms

prune22.0ms

localize11.0ms

rewrite32.0ms

series78.0ms

simplify43.0ms

prune158.0ms

localize11.0ms

rewrite40.0ms

series124.0ms

simplify67.0ms

prune192.0ms

localize11.0ms

rewrite26.0ms

series83.0ms

simplify40.0ms

prune111.0ms

localize10.0ms

rewrite41.0ms

series72.0ms

simplify59.0ms

prune135.0ms

regimes321.0ms

bsearch79.0ms

simplify1.0ms

end0.0ms

sample1.5s

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