Details

analyze466.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample47.0ms

Algorithm

intervals

Results

12.0ms	39×	body	2560	valid
9.0ms	157×	body	80	valid
7.0ms	27×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	23×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	14×	body	80	invalid
1.0ms	6×	body	160	valid

simplify177.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (176.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 36.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

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 → 69

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)))

series66.0ms

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

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5899	1226

prune165.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	70	11	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	11	82

Merged error: 7.4b

Counts

82 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
3.4b	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
13.7b	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
24.3b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite46.0ms

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 → 119

Calls

4 calls:

10.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
16.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
13.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
45.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
54.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify69.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4973	2553
1	4973	2553

prune190.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	131	11	142

Merged error: 7.3b

Counts

142 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.4b	(- (* b b) (* 3.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
24.3b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite22.0ms

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 → 61

Calls

4 calls:

5.0ms	(* 3.0 (* a c))
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))))

series42.0ms

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)))))
15.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4956	873
1	4956	873

prune128.0ms

Filtered

51 candidates to 73 candidates (-43.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	73	11	84

Merged error: 7.0b

Counts

84 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* c (cbrt 3.0))
0.4b	(- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0)))))
1.0b	(- (neg b) (sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0)))))))
24.3b	(sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

5.0ms	(* c (cbrt 3.0))
4.0ms	(- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0)))))
9.0ms	(- (neg b) (sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0)))))))
4.0ms	(sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0))))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* c (cbrt 3.0))
12.0ms	(- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0)))))
20.0ms	(- (neg b) (sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0)))))))
19.0ms	(sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4891	889
1	4891	889

prune121.0ms

Filtered

59 candidates to 77 candidates (-30.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	77	11	88

Merged error: 7.0b

Counts

88 → 11

regimes358.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.6b against oracle of 5.3b and baseline of 29.5b

bsearch86.0ms

Steps

Iters	Range	Point
7	1.5076119834637862e+100	3.066974460136245e+102	1.100584786088886e+102
7	-5.415287738518792e-236	-7.260025944858288e-238	-2.3344782568300924e-237
9	-1.1147125825604471e+110	-2.6689805155627756e+100	-6.845054683259517e+108

Iters

Range

Point

1.5076119834637862e+100

3.066974460136245e+102

1.100584786088886e+102

-5.415287738518792e-236

-7.260025944858288e-238

-2.3344782568300924e-237

-1.1147125825604471e+110

-2.6689805155627756e+100

-6.845054683259517e+108

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	234	89
1	234	89

end0.0ms

sample1.4s

Algorithm

intervals

Results

348.0ms	1058×	body	2560	valid
291.0ms	5038×	body	80	valid
263.0ms	963×	body	1280	valid
99.0ms	463×	body	640	valid
56.0ms	137×	body	5120	valid
35.0ms	647×	body	80	nan
34.0ms	213×	body	320	valid
23.0ms	373×	body	80	invalid
13.0ms	128×	body	160	valid

Details

analyze466.0ms

sample47.0ms

simplify177.0ms

prune8.0ms

localize14.0ms

rewrite29.0ms

series66.0ms

simplify42.0ms

prune165.0ms

localize13.0ms

rewrite46.0ms

series127.0ms

simplify69.0ms

prune190.0ms

localize13.0ms

rewrite22.0ms

series42.0ms

simplify46.0ms

prune128.0ms

localize18.0ms

rewrite24.0ms

series57.0ms

simplify51.0ms

prune121.0ms

regimes358.0ms

bsearch86.0ms

simplify3.0ms

end0.0ms

sample1.4s

Profiling