Details

sample42.0ms

Algorithm

intervals

Results

7.0ms	189×	body	80	valid
7.0ms	37×	body	1280	valid
6.0ms	27×	body	2560	valid
4.0ms	98×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite103.0ms

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:

63.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
71.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
39.0ms	(- (* b b) (* (* 4.0 a) c))
63.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

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

prune221.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
2.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite162.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
55.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 4.0 a) c))
129.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
168.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
65.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (87.0ms)

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

prune410.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize19.0ms

Local error

Found 4 expressions with local error:

7.1b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
8.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))
21.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
4×	`pow1` `cbrt-div` `flip3--` `flip--`
3×	`associate-/r` `associate-/l`
2×	`pow1/3` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 71

Calls

4 calls:

11.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
32.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series831.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
570.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))
90.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
90.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify100.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	632	1757
1	3011	1587
2	5003	1579

prune416.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

7.1b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
7.9b	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))))
21.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `cbrt-prod`
4×	`cbrt-div` `flip3--` `prod-exp` `flip--`
3×	`associate-l` `unswap-sqr`
2×	`frac-times` `flip3-+` `pow1/3` `diff-log` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 82

Calls

4 calls:

12.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
49.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series799.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
538.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))))
89.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
92.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify166.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	740	1859
1	4030	1641
2	5001	1618

prune398.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.5b

regimes237.0ms

Accuracy

86.1% (3.7b remaining)

Error of 9.3b against oracle of 5.6b and baseline of 32.0b

bsearch198.0ms

Steps

Iters	Range		Point
9	1.074100872074174e-14	9.291103138484119e-07	9.167997088350656e-07
7	2.2469575477562033e-86	4.474843512735295e-85	2.2742398392973687e-86
9	-3.3947692407777386e+132	-4.222463702829868e+123	-8.50694614622187e+125

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	29
1	52	29
2	52	29

end0.0ms

sample1.2s

Algorithm

intervals

Results

243.0ms	1096×	body	2560	valid
227.0ms	5864×	body	80	valid
170.0ms	913×	body	1280	valid
110.0ms	3005×	body	80	nan
75.0ms	459×	body	640	valid
30.0ms	101×	body	5120	valid
25.0ms	212×	body	320	valid
9.0ms	125×	body	160	valid