Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	197×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	90×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

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:

37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune234.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
3.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
144.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	640	2579
1	3155	2333
2	5001	2320

prune431.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize21.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
3.7b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
8.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`sqrt-prod`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `distribute-rgt-neg-in` `associate-r` `associate-/r*`
6×	`add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 143

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
65.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
147.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
186.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify135.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	732	2302
1	3924	1975
2	5003	1968

prune412.0ms

Filtered

155 candidates to 99 candidates (63.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
15.1b	(/ (* 4.0 (* a c)) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(/ (* 4.0 (* a c)) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(- (* b b) (* (* 4.0 a) c))
149.0ms	(/ (* 4.0 (* a c)) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify96.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	565	1153
1	3763	861
2	5002	861

prune206.0ms

Filtered

90 candidates to 57 candidates (63.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.6b

regimes195.0ms

Accuracy

83.8% (4.3b remaining)

Error of 9.6b against oracle of 5.3b and baseline of 31.8b

bsearch135.0ms

Steps

Iters	Range		Point
9	3.2956103981062554e-86	3.6842556330088986e-79	2.267195199467958e-82
11	-1.7053146236540368e+120	-1.0719231849388273e+91	-3.5940112039867074e+100

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

248.0ms	1080×	body	2560	valid
232.0ms	5783×	body	80	valid
182.0ms	928×	body	1280	valid
113.0ms	2980×	body	80	nan
71.0ms	450×	body	640	valid
29.0ms	105×	body	5120	valid
29.0ms	258×	body	320	valid
9.0ms	123×	body	160	valid