Details

sample62.0ms

Algorithm

intervals

Results

11.0ms	33×	body	2560	valid
10.0ms	176×	body	80	valid
8.0ms	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
1.0ms	5×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	88	16
1	88	16

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 35.3b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.5b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
9.0ms	(- (* b b) (* (* 3.0 a) c))
19.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4953	1232
1	4953	1232

prune182.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	73	11	84

Merged error: 5.7b

Counts

84 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 3.0 (* a c)))
3.8b	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
10.0b	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
21.5b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
34×	`times-frac`
28×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
7×	`sqrt-prod`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`distribute-rgt-neg-in` `div-inv`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

4.0ms	(- (* b b) (* 3.0 (* a c)))
20.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
15.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
5.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series139.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 3.0 (* a c)))
47.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
66.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
16.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify35.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5589	2404

prune203.0ms

Filtered

79 candidates to 126 candidates (-59.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	125	12	137

Merged error: 5.5b

Counts

137 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.6b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
1.0b	(- (* b b) (* 3.0 (* a c)))
21.5b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `associate-r` `neg-log` `*-commutative`

Counts

4 → 63

Calls

4 calls:

6.0ms	(* 3.0 (* a c))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* 3.0 (* a c))
17.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
10.0ms	(- (* b b) (* 3.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify40.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4969	890
1	4969	890

prune131.0ms

Filtered

51 candidates to 75 candidates (-47.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	75	12	87

Merged error: 5.5b

Counts

87 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))))
1.0b	(- (* b b) (* 3.0 (* a c)))
16.6b	(* (* a c) (/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))))
21.5b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-exp-log`
30×	`prod-exp` `add-cbrt-cube`
13×	`pow1`
12×	`div-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`cbrt-undiv` `rec-exp` `times-frac` `1-exp` `add-log-exp`
5×	`associate-*r/`
4×	`flip3--` `pow-prod-down` `associate-/r/` `flip--`
3×	`sqrt-prod` `associate-/l*`
2×	`pow-flip` `sqrt-div` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `associate-/r` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 99

Calls

4 calls:

12.0ms	(/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))))
4.0ms	(- (* b b) (* 3.0 (* a c)))
17.0ms	(* (* a c) (/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series122.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))))
9.0ms	(- (* b b) (* 3.0 (* a c)))
48.0ms	(* (* a c) (/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))))
16.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4989	1561
1	4989	1561

prune120.0ms

Filtered

64 candidates to 111 candidates (-73.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	8	9
Picked	1	0	1
Done	0	2	2
Total	112	11	123

Merged error: 5.5b

Counts

123 → 11

regimes614.0ms

Accuracy

95% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.5b

bsearch100.0ms

Steps

Iters	Range	Point
6	1.1487243557305423e+102	6.148420459531844e+102	2.5626360877386485e+102
8	-7.67443757966827e-305	8.126837495347253e-308	-2.319419628282691e-305
10	-8.003596903883499e+165	-5.641302321031635e+152	-5.98287245126569e+153

Iters

Range

Point

1.1487243557305423e+102

6.148420459531844e+102

2.5626360877386485e+102

-7.67443757966827e-305

8.126837495347253e-308

-2.319419628282691e-305

-8.003596903883499e+165

-5.641302321031635e+152

-5.98287245126569e+153

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	64
1	52	64

end0.0ms

sample1.7s

Algorithm

intervals

Results

347.0ms	1070×	body	2560	valid
329.0ms	5828×	body	80	valid
238.0ms	906×	body	1280	valid
162.0ms	2970×	body	80	nan
100.0ms	484×	body	640	valid
54.0ms	129×	body	5120	valid
31.0ms	200×	body	320	valid
11.0ms	102×	body	160	valid

Details

sample62.0ms

simplify3.0ms

prune11.0ms

localize11.0ms

rewrite30.0ms

series72.0ms

simplify51.0ms

prune182.0ms

localize13.0ms

rewrite48.0ms

series139.0ms

simplify35.0ms

prune203.0ms

localize13.0ms

rewrite25.0ms

series49.0ms

simplify40.0ms

prune131.0ms

localize13.0ms

rewrite41.0ms

series122.0ms

simplify39.0ms

prune120.0ms

regimes614.0ms

bsearch100.0ms

simplify1.0ms

end0.0ms

sample1.7s

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