Details

sample65.0ms

Algorithm

intervals

Results

16.0ms	42×	body	2560	valid
14.0ms	186×	body	80	valid
7.0ms	23×	body	1280	valid
5.0ms	79×	body	80	nan
3.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	5120	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

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 b) (* 4.0 (* a c)))
2.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

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:

35.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
5.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(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

prune243.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* 4.0 (* a c)))
2.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite82.0ms

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:

60.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
43.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (49.0ms)

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

prune226.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
14.6b	(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
15.8b	(- (pow b 2) (pow b 2))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`add-exp-log`
22×	`unpow-prod-down`
20×	`*-un-lft-identity`
16×	`add-cube-cbrt` `difference-of-squares`
13×	`add-cbrt-cube`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--` `prod-exp`
8×	`distribute-lft-out--` `add-log-exp`
7×	`pow1` `associate-l`
4×	`div-exp` `cbrt-unprod`
3×	`flip3--` `times-frac` `associate-r` `sqrt-prod` `flip--`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `flip3-+` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `flip-+`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `+-inverses` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
192.0ms	(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
11.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
1.0ms	(- (pow b 2) (pow b 2))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify317.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (308.0ms)

Iter	Nodes	Cost
0	591	781
1	4612	569
2	5001	561

prune294.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.3b	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

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-/r*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

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

series392.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
193.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	366	755
1	1482	656
2	5001	644

prune184.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 5.3b

regimes235.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.8b

bsearch209.0ms

Steps

Iters	Range	Point
9	1.0966316111626227e+109	8.247031634266059e+117	3.8150823398629306e+117
8	3.067319068746414e-261	9.772075720105142e-259	1.421516483922834e-260
8	-5.769371586257069e+162	-2.0426714906170593e+160	-2.0650509315772598e+160

Iters

Range

Point

1.0966316111626227e+109

8.247031634266059e+117

3.8150823398629306e+117

3.067319068746414e-261

9.772075720105142e-259

1.421516483922834e-260

-5.769371586257069e+162

-2.0426714906170593e+160

-2.0650509315772598e+160

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	40	24

end0.0ms

sample1.8s

Algorithm

intervals

Results

446.0ms	5878×	body	80	valid
408.0ms	1066×	body	2560	valid
280.0ms	892×	body	1280	valid
212.0ms	2992×	body	80	nan
108.0ms	445×	body	640	valid
51.0ms	115×	body	5120	valid
41.0ms	222×	body	320	valid
15.0ms	117×	body	160	valid