Details

sample89.0ms

Algorithm

intervals

Results

20.0ms	183×	body	80	valid
19.0ms	33×	body	2560	valid
14.0ms	31×	body	1280	valid
9.0ms	85×	body	80	nan
6.0ms	17×	body	640	valid
3.0ms	10×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite52.0ms

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) (* (* 3.0 a) c)))) (* 3.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune223.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.7b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
13.1b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite84.0ms

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:

2.0ms	(- (* b b) (* (* 3.0 a) c))
42.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
29.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
147.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
180.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
98.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	635	2579
1	3125	2333
2	5001	2320

prune408.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
15.4b	(/ (* 3.0 a) (* 3.0 (* a c)))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
13.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	417	636
1	2439	522
2	5001	492

prune207.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

27.0ms	(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
14.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
50.0ms	(- (* b b) (* (* 3.0 a) c))
79.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	432	926
1	1830	797
2	5003	784

prune205.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

regimes190.0ms

Accuracy

95.1% (1.2b remaining)

Error of 7.0b against oracle of 5.8b and baseline of 29.8b

bsearch195.0ms

Steps

Iters	Range	Point
8	3.182319375801986e+130	1.3165557463351014e+133	3.656065219850042e+131
8	-7.043002195311016e-204	-2.3385896676979497e-206	-1.202999495221249e-205
8	-3.739307379384431e+110	-1.120612400025049e+108	-8.867258777411048e+108

Iters

Range

Point

3.182319375801986e+130

1.3165557463351014e+133

3.656065219850042e+131

-7.043002195311016e-204

-2.3385896676979497e-206

-1.202999495221249e-205

-3.739307379384431e+110

-1.120612400025049e+108

-8.867258777411048e+108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	27
1	47	27

end0.0ms

sample1.7s

Algorithm

intervals

Results

421.0ms	5876×	body	80	valid
375.0ms	1068×	body	2560	valid
257.0ms	881×	body	1280	valid
189.0ms	2896×	body	80	nan
106.0ms	446×	body	640	valid
43.0ms	103×	body	5120	valid
38.0ms	222×	body	320	valid
14.0ms	114×	body	160	valid