Details

sample56.0ms

Algorithm

intervals

Results

12.0ms	44×	body	2560	valid
8.0ms	169×	body	80	valid
8.0ms	33×	body	1280	valid
4.0ms	89×	body	80	nan
3.0ms	15×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	8×	body	320	valid
1.0ms	9×	body	160	valid

simplify173.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (172.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 38.2b

Counts

2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.2b	(- (* b b) (* (* 3.0 a) c))
1.7b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
26.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

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:

12.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5899	1232

prune181.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	71	13	84

Merged error: 6.2b

Counts

84 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
3.6b	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
12.7b	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
26.0b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

9.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
17.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
16.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
44.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
57.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify74.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4973	2564
1	4973	2564

prune242.0ms

Filtered

84 candidates to 132 candidates (-57.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	132	13	145

Merged error: 6.1b

Counts

145 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
1.2b	(- (* b b) (* 3.0 (* a c)))
1.8b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
26.0b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

5.0ms	(* 3.0 (* a c))
4.0ms	(- (* b b) (* 3.0 (* a c)))
11.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
8.0ms	(- (* b b) (* 3.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4956	890
1	4956	890

prune176.0ms

Filtered

51 candidates to 75 candidates (-47.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	74	14	88

Merged error: 5.9b

Counts

88 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.5 (* c (/ a b))) (* b -2))
0.3b	(* 1.5 (* c (/ a b)))
3.3b	(/ c (+ (* 1.5 (* c (/ a b))) (* b -2)))
4.4b	(* c (/ a b))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `add-cbrt-cube`
19×	`times-frac`
14×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`pow-prod-down`
3×	`cbrt-undiv` `associate-r/` `div-exp` `associate-/r` `associate-/l*`
2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `div-inv` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `clear-num` `sum-log`

Counts

4 → 93

Calls

4 calls:

8.0ms	(+ (* 1.5 (* c (/ a b))) (* b -2))
6.0ms	(* 1.5 (* c (/ a b)))
9.0ms	(/ c (+ (* 1.5 (* c (/ a b))) (* b -2)))
7.0ms	(* c (/ a b))

series38.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (* 1.5 (* c (/ a b))) (* b -2))
5.0ms	(* 1.5 (* c (/ a b)))
15.0ms	(/ c (+ (* 1.5 (* c (/ a b))) (* b -2)))
5.0ms	(* c (/ a b))

simplify74.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5580	1206

prune148.0ms

Filtered

75 candidates to 105 candidates (-40.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	104	15	119

Merged error: 5.9b

Counts

119 → 15

regimes498.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.9b against oracle of 5.5b and baseline of 29.9b

bsearch80.0ms

Steps

Iters	Range	Point
5	1.1994113433831075e+59	2.551497614016684e+59	1.9930311221408239e+59
7	-1.5288248722247393e-196	-2.8030120978369076e-198	-2.8405866436241524e-198
8	-9.755383452814402e+129	-1.823895620004969e+126	-1.95155870856424e+129

Iters

Range

Point

1.1994113433831075e+59

2.551497614016684e+59

1.9930311221408239e+59

-1.5288248722247393e-196

-2.8030120978369076e-198

-2.8405866436241524e-198

-9.755383452814402e+129

-1.823895620004969e+126

-1.95155870856424e+129

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	150	87
1	150	87

end0.0ms

sample1.6s

Algorithm

intervals

Results

326.0ms	1080×	body	2560	valid
300.0ms	5799×	body	80	valid
213.0ms	887×	body	1280	valid
146.0ms	2932×	body	80	nan
85.0ms	456×	body	640	valid
36.0ms	258×	body	320	valid
35.0ms	99×	body	5120	valid
11.0ms	119×	body	160	valid

Details

sample56.0ms

simplify173.0ms

prune11.0ms

localize13.0ms

rewrite30.0ms

series65.0ms

simplify42.0ms

prune181.0ms

localize13.0ms

rewrite50.0ms

series130.0ms

simplify74.0ms

prune242.0ms

localize12.0ms

rewrite25.0ms

series41.0ms

simplify46.0ms

prune176.0ms

localize10.0ms

rewrite32.0ms

series38.0ms

simplify74.0ms

prune148.0ms

regimes498.0ms

bsearch80.0ms

simplify2.0ms

end0.0ms

sample1.6s

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