Details

sample45.0ms

Algorithm

intervals

Results

10.0ms	33×	body	2560	valid
8.0ms	197×	body	80	valid
5.0ms	27×	body	1280	valid
4.0ms	116×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	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: 32.8b

localize12.0ms

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)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

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:

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))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* 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

prune240.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

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:

3.0ms	(- (* b b) (* 4.0 (* a c)))
56.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* 4.0 (* a c)))
95.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (48.0ms)

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

prune230.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite52.0ms

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:

29.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
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))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (52.0ms)

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

prune262.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0b	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
17.5b	(- (pow b 2) (pow b 2))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`unpow-prod-down`
19×	`add-exp-log`
16×	`difference-of-squares`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--` `add-log-exp`
8×	`distribute-lft-out--`
7×	`div-exp`
5×	`pow1` `associate-/l/`
4×	`cbrt-undiv` `prod-exp`
3×	`flip3-+` `times-frac` `associate-/r*` `sqrt-prod` `flip-+`
2×	`frac-times` `flip3--` `sqrt-div` `associate-*r/` `sum-log` `flip--` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `+-inverses` `diff-log` `1-exp` `neg-log` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 107

Calls

4 calls:

11.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
11.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
1.0ms	(- (pow b 2) (pow b 2))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify196.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (187.0ms)

Iter	Nodes	Cost
0	595	778
1	3991	571
2	5002	555

prune317.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

regimes192.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.8b

bsearch192.0ms

Steps

Iters	Range	Point
9	2.6683347110001497e+63	3.895668027475672e+69	3.826558553654448e+69
7	-3.4381592348580506e-280	-2.6562521403830515e-282	-2.7034426964320083e-282
9	-1.2294333374423815e+100	-1.4471431684397531e+91	-8.829790255688243e+98

Iters

Range

Point

2.6683347110001497e+63

3.895668027475672e+69

3.826558553654448e+69

-3.4381592348580506e-280

-2.6562521403830515e-282

-2.7034426964320083e-282

-1.2294333374423815e+100

-1.4471431684397531e+91

-8.829790255688243e+98

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample1.2s

Algorithm

intervals

Results

258.0ms	1047×	body	2560	valid
235.0ms	5813×	body	80	valid
179.0ms	932×	body	1280	valid
107.0ms	2901×	body	80	nan
70.0ms	470×	body	640	valid
37.0ms	110×	body	5120	valid
25.0ms	220×	body	320	valid
9.0ms	120×	body	160	valid