Details

sample64.0ms

Algorithm

intervals

Results

15.0ms	40×	body	2560	valid
14.0ms	185×	body	80	valid
8.0ms	25×	body	1280	valid
5.0ms	22×	body	640	valid
5.0ms	72×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	3×	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	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.2b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

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:

33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(+ (- 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:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms	(- (* b b) (* 4.0 (* a c)))
82.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune230.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
5.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite82.0ms

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:

3.0ms	(- (* b b) (* 4.0 (* a c)))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
25.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* 4.0 (* a c)))
150.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
186.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	628	2579
1	2954	2333
2	5001	2320

prune595.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* b b) (- 0 (* 4.0 (* a c))))
5.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
11.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))
22.5b	(sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))

rewrite135.0ms

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`
9×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`div-inv`
3×	`flip3--` `flip3-+` `flip--` `flip-+` `associate-/l/`
2×	`associate-+r+` `frac-2neg` `sub0-neg` `sqrt-div` `prod-exp` `clear-num` `sum-log` `cbrt-unprod`
1×	`+-commutative` `associate-+r-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `unsub-neg`

Counts

4 → 153

Calls

4 calls:

6.0ms	(+ (* b b) (- 0 (* 4.0 (* a c))))
67.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
46.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))
9.0ms	(sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* b b) (- 0 (* 4.0 (* a c))))
148.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
178.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))
71.0ms	(sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))

simplify113.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	646	2793
1	3132	2522
2	5001	2507

prune426.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.2b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

53.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
50.0ms	(- (* b b) (* 4.0 (* a c)))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify61.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	479	921
1	2139	790
2	5002	777

prune227.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.6b

regimes225.0ms

Accuracy

81.7% (5.0b remaining)

Error of 10.6b against oracle of 5.5b and baseline of 33.1b

bsearch116.0ms

Steps

Iters	Range		Point
7	4.3988303560488366e-111	1.0767117479383607e-108	1.0502924240289742e-108
8	-1.0362695438716464e+73	-8.682929093782064e+69	-2.9644058459680186e+71

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	38	16

end0.0ms

sample1.8s

Algorithm

intervals

Results

461.0ms	5897×	body	80	valid
413.0ms	1096×	body	2560	valid
260.0ms	835×	body	1280	valid
209.0ms	2915×	body	80	nan
116.0ms	461×	body	640	valid
52.0ms	106×	body	5120	valid
45.0ms	231×	body	320	valid
14.0ms	109×	body	160	valid