Details

sample61.0ms

Algorithm

intervals

Results

15.0ms	47×	body	2560	valid
11.0ms	167×	body	80	valid
9.0ms	32×	body	1280	valid
6.0ms	107×	body	80	nan
3.0ms	16×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	6×	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: 35.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.2b	(- (* b b) (* (* 3.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
2.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
47.0ms	(- (* b b) (* (* 3.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune183.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
4.6b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.6b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.7b	(sqrt (- (* b b) (* (* 3.0 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) (* (* 3.0 a) c))
44.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
26.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 3.0 a) c))
141.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
173.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (88.0ms)

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

prune420.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.0b

localize27.0ms

Local error

Found 4 expressions with local error:

13.9b	(cbrt (+ 0 (* 3.0 (* a c))))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 58

Calls

4 calls:

2.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	259	537
1	1023	510
2	5001	498

prune409.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.0b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* b b) (- 0 (* 3.0 (* a c))))
4.6b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c))))))) (* 3.0 a))
9.6b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))))
22.7b	(sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))

rewrite138.0ms

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 (* 3.0 (* a c))))
72.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c))))))) (* 3.0 a))
44.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))))
9.0ms	(sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* b b) (- 0 (* 3.0 (* a c))))
152.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c))))))) (* 3.0 a))
187.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))))
73.0ms	(sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	644	2793
1	3121	2522
2	5002	2507

prune409.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.0b

regimes409.0ms

Accuracy

94.7% (1.1b remaining)

Error of 12.4b against oracle of 11.3b and baseline of 31.7b

bsearch219.0ms

Steps

Iters	Range	Point
6	5.779436182351587e+124	6.964873849469576e+125	6.771165814787109e+125
8	3.5242701449549723e-134	2.7035586924523766e-131	1.381900373008268e-133
12	-7.927726045730789e+181	-4.544878892552954e+140	-1.3379185299605649e+154

Iters

Range

Point

5.779436182351587e+124

6.964873849469576e+125

6.771165814787109e+125

3.5242701449549723e-134

2.7035586924523766e-131

1.381900373008268e-133

-7.927726045730789e+181

-4.544878892552954e+140

-1.3379185299605649e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	36
1	59	36
2	65	36
3	65	36

end0.0ms

sample1.7s

Algorithm

intervals

Results

391.0ms	5746×	body	80	valid
382.0ms	1107×	body	2560	valid
260.0ms	929×	body	1280	valid
180.0ms	2804×	body	80	nan
107.0ms	479×	body	640	valid
44.0ms	106×	body	5120	valid
36.0ms	215×	body	320	valid
14.0ms	118×	body	160	valid