Details

sample43.0ms

Algorithm

intervals

Results

10.0ms	45×	body	2560	valid
6.0ms	170×	body	80	valid
6.0ms	31×	body	1280	valid
4.0ms	99×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	5×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune3.0ms

Filtered

1 candidates to 0 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: 35.4b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

11.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
51.0ms	(- (* b b) (* 4.0 (* a c)))
98.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune227.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	8	90

Merged error: 6.1b

Counts

90 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

15.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
46.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857

prune202.0ms

Filtered

97 candidates to 64 candidates (66.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	98	7	105

Merged error: 6.1b

Counts

105 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.1b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

11.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms	(- (* b b) (* 4.0 (* a c)))
162.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify100.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	502	969
1	3079	812
2	5002	794

prune206.0ms

Filtered

83 candidates to 63 candidates (75.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	81	9	90

Merged error: 6.0b

Counts

90 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
16.7b	(/ (/ (* 4.0 (* a c)) 2.0) a)
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

10.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series200.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify70.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	543	780
1	2606	706
2	5001	702

prune252.0ms

Filtered

104 candidates to 79 candidates (76.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	2	3	5
Picked	1	0	1
Done	0	3	3
Total	105	8	113

Merged error: 6.0b

Counts

113 → 8

regimes250.0ms

Accuracy

94.2% (1.4b remaining)

Error of 6.8b against oracle of 5.4b and baseline of 29.6b

bsearch155.0ms

Steps

Iters	Range		Point
8	3.6696373663460875e+72	1.716395662560696e+75	1.4190020934043307e+75
9	3.2808637056084806e-251	2.232588100468634e-246	1.0566253921447251e-248
5	-9.311037300204504e+81	-3.7745034531398073e+81	-9.164316609452024e+81

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	25
1	45	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

249.0ms	5952×	body	80	valid
240.0ms	1018×	body	2560	valid
170.0ms	886×	body	1280	valid
107.0ms	2961×	body	80	nan
67.0ms	446×	body	640	valid
33.0ms	115×	body	5120	valid
27.0ms	221×	body	320	valid
8.0ms	105×	body	160	valid