Details

sample42.0ms

Algorithm

intervals

Results

8.0ms	34×	body	2560	valid
7.0ms	186×	body	80	valid
6.0ms	32×	body	1280	valid
3.0ms	94×	body	80	nan
3.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	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: 36.2b

localize13.0ms

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)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

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:

16.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

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

prune252.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

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

series315.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
87.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify66.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	533	1804
1	2544	1605
2	5002	1531

prune255.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

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×	`sub-neg` `div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `rec-exp` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-div` `1-exp` `associate-*r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

16.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	475	1025
1	2257	896
2	5001	893

prune235.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
5.6b	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
23.1b	(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`add-cube-cbrt` `log-prod` `exp-sum`
7×	`pow1` `sqrt-prod`
6×	`exp-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
3×	`diff-log` `log-pow` `difference-of-squares`
2×	`sub-neg` `log-div` `sqrt-pow1` `pow1/2` `exp-diff` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `neg-log` `rem-exp-log`

Counts

4 → 68

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
6.0ms	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series269.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* 4.0 (* a c)))
68.0ms	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
79.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify112.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	275	713
1	910	655
2	3688	628
3	5001	615

prune224.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.0b

regimes211.0ms

Accuracy

88% (3.4b remaining)

Error of 9.2b against oracle of 5.7b and baseline of 34.3b

bsearch142.0ms

Steps

Iters	Range		Point
3	5.062782482725967e+112	6.853081242536654e+112	6.293612880095814e+112
7	-2.1605152142522817e-113	-1.8017938791730603e-115	-2.125553485370055e-113
5	-1.1619433740097673e-94	-3.191731313316827e-95	-6.180620892104376e-95
4	-2.1402528215307472e+20	-1.2933083028149787e+20	-1.8507408941501855e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	34
1	55	34

end0.0ms

sample1.2s

Algorithm

intervals

Results

254.0ms	1069×	body	2560	valid
230.0ms	5857×	body	80	valid
176.0ms	907×	body	1280	valid
106.0ms	2908×	body	80	nan
70.0ms	468×	body	640	valid
32.0ms	95×	body	5120	valid
29.0ms	244×	body	320	valid
9.0ms	115×	body	160	valid