Details

sample48.0ms

Algorithm

intervals

Results

10.0ms	204×	body	80	valid
8.0ms	29×	body	2560	valid
6.0ms	25×	body	1280	valid
5.0ms	98×	body	80	nan
3.0ms	15×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune3.0ms

Filtered

1 candidates to 0 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: 31.3b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune227.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	9	90

Merged error: 5.2b

Counts

90 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

15.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
81.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857

prune219.0ms

Filtered

97 candidates to 64 candidates (66.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	96	10	106

Merged error: 5.2b

Counts

106 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

17.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
80.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
50.0ms	(- (* b b) (* 4.0 (* a c)))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify70.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	533	1802
1	2544	1603
2	5002	1529

prune224.0ms

Filtered

137 candidates to 71 candidates (51.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	139	8	147

Merged error: 5.2b

Counts

147 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
13.9b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series371.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
171.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify106.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	502	969
1	3028	812
2	5001	794

prune203.0ms

Filtered

83 candidates to 62 candidates (74.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	82	9	91

Merged error: 5.2b

Counts

91 → 9

regimes215.0ms

Accuracy

89% (3.1b remaining)

Error of 8.8b against oracle of 5.7b and baseline of 34.1b

bsearch210.0ms

Steps

Iters	Range	Point
10	1.4182100026226751e+88	1.1634796338171106e+98	4.5720489322241335e+94
7	-2.6653979660135254e-122	-1.1110532800434707e-124	-1.6086867020358568e-124
9	-2.112079485172501e+81	-7.412295145025422e+71	-3.595919917945398e+76

Iters

Range

Point

1.4182100026226751e+88

1.1634796338171106e+98

4.5720489322241335e+94

-2.6653979660135254e-122

-1.1110532800434707e-124

-1.6086867020358568e-124

-2.112079485172501e+81

-7.412295145025422e+71

-3.595919917945398e+76

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	33
1	52	33

end0.0ms

sample1.4s

Algorithm

intervals

Results

345.0ms	1107×	body	2560	valid
307.0ms	5833×	body	80	valid
221.0ms	903×	body	1280	valid
146.0ms	2897×	body	80	nan
88.0ms	438×	body	640	valid
40.0ms	105×	body	5120	valid
32.0ms	216×	body	320	valid
11.0ms	111×	body	160	valid

Details

sample48.0ms

simplify14.0ms

prune3.0ms

localize12.0ms

rewrite32.0ms

series295.0ms

simplify46.0ms

prune227.0ms

localize13.0ms

rewrite33.0ms

series302.0ms

simplify57.0ms

prune219.0ms

localize12.0ms

rewrite37.0ms

series314.0ms

simplify70.0ms

prune224.0ms

localize15.0ms

rewrite32.0ms

series371.0ms

simplify106.0ms

prune203.0ms

regimes215.0ms

bsearch210.0ms

simplify2.0ms

end0.0ms

sample1.4s

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