Details

sample73.0ms

Algorithm

intervals

Results

19.0ms	181×	body	80	valid
16.0ms	38×	body	2560	valid
10.0ms	31×	body	1280	valid
5.0ms	66×	body	80	nan
4.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune300.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
27.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
154.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
184.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify139.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	829	5119
1	3763	3863
2	5001	3860

prune564.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.2b	(/ (* 2.0 a) (* 4.0 (* a c)))
24.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-exp-log`
63×	`add-cbrt-cube`
60×	`prod-diff`
57×	`prod-exp`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`div-exp`
34×	`sqrt-prod`
25×	`cbrt-unprod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
20×	`cbrt-undiv`
10×	`fma-neg`
8×	`pow1` `rec-exp` `1-exp` `add-log-exp`
7×	`neg-mul-1`
5×	`associate-/r/`
4×	`expm1-log1p-u` `flip3--` `times-frac` `flip--` `log1p-expm1-u` `associate-/l*`
2×	`frac-times` `pow-flip` `frac-2neg` `sqrt-div` `diff-log` `associate-r/` `clear-num` `associate-/r` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-*l/` `inv-pow`

Counts

4 → 193

Calls

4 calls:

65.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify143.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	915	3956
1	4836	2570
2	5001	2570

prune358.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (/ 2.0 4.0) 1) c))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
291×	`add-sqr-sqrt`
290×	`*-un-lft-identity`
190×	`add-cube-cbrt`
94×	`add-exp-log`
64×	`div-exp`
61×	`prod-diff`
58×	`sqrt-prod`
50×	`distribute-lft-out--` `difference-of-squares`
46×	`distribute-rgt-neg-in`
37×	`div-inv`
36×	`add-cbrt-cube`
27×	`associate-/l*`
21×	`distribute-lft-neg-in`
20×	`cbrt-undiv`
17×	`associate-/r/`
16×	`prod-exp`
14×	`1-exp`
11×	`flip3--` `fma-neg` `flip--`
10×	`add-log-exp`
7×	`neg-mul-1` `associate-/r*`
6×	`rec-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 392

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (/ 2.0 4.0) 1) c))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
126.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (/ 2.0 4.0) 1) c))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify93.0ms

Algorithm

egg-herbie

Counts

404 → 404

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1597	8817
1	5002	7331

prune705.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

regimes182.0ms

Accuracy

79% (5.0b remaining)

Error of 11.0b against oracle of 6.0b and baseline of 30.0b

bsearch329.0ms

Steps

Iters	Range		Point
10	9.168682727753708e+124	1.4581761209996442e+140	6.972127475937741e+134
10	-4.4698229087150014e-60	-7.90650715848996e-79	-3.097985126053574e-61
10	-1.003617951747773e+25	-9531903230471.172	-9.847501781463365e+24
7	-1.4072277076308412e+56	-5.8205596871901896e+54	-5.874864305580093e+54

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	43
1	70	43
2	70	43

end0.0ms

sample2.0s

Algorithm

intervals

Results

512.0ms	5833×	body	80	valid
456.0ms	1077×	body	2560	valid
301.0ms	856×	body	1280	valid
219.0ms	2698×	body	80	nan
129.0ms	464×	body	640	valid
49.0ms	96×	body	5120	valid
47.0ms	223×	body	320	valid
17.0ms	104×	body	160	valid