Details

sample55.0ms

Algorithm

intervals

Results

14.0ms	39×	body	2560	valid
9.0ms	180×	body	80	valid
8.0ms	35×	body	1280	valid
5.0ms	98×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	4×	body	5120	valid
0.0ms	2×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	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: 33.5b

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))
0.9b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

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:

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

series305.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
79.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune205.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 5.3b

Counts

83 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
3.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.4b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite41.0ms

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:

4.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* 4.0 (* a c)))
151.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
181.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify108.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	628	2579
1	2921	2333
2	5002	2320

prune352.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	158	10	168

Merged error: 5.3b

Counts

168 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
15.5b	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

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×	`flip3--` `sqrt-prod` `flip--`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `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 → 72

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
151.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify68.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	469	942
1	2644	746
2	5001	738

prune188.0ms

Filtered

84 candidates to 58 candidates (69.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	85	9	94

Merged error: 5.3b

Counts

94 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c))
0.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

12.0ms	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 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))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c))
75.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	538	1186
1	2211	1070
2	5001	1069

prune244.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	107	8	115

Merged error: 5.3b

Counts

115 → 8

regimes171.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.4b

bsearch214.0ms

Steps

Iters	Range	Point
10	1.4182100026226751e+88	1.1634796338171106e+98	1.0100267697287914e+93
10	-1.907966459858268e-129	-3.039489316543787e-144	-3.100973882795572e-144
7	-3.394702059408153e+117	-4.3501158911079625e+115	-3.631154114249338e+116

Iters

Range

Point

1.4182100026226751e+88

1.1634796338171106e+98

1.0100267697287914e+93

-1.907966459858268e-129

-3.039489316543787e-144

-3.100973882795572e-144

-3.394702059408153e+117

-4.3501158911079625e+115

-3.631154114249338e+116

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	27
1	48	27

end0.0ms

sample1.4s

Algorithm

intervals

Results

313.0ms	1057×	body	2560	valid
303.0ms	5923×	body	80	valid
205.0ms	871×	body	1280	valid
143.0ms	2904×	body	80	nan
81.0ms	437×	body	640	valid
41.0ms	112×	body	5120	valid
34.0ms	232×	body	320	valid
10.0ms	108×	body	160	valid

Details

sample55.0ms

simplify12.0ms

prune3.0ms

localize12.0ms

rewrite28.0ms

series305.0ms

simplify45.0ms

prune205.0ms

localize17.0ms

rewrite41.0ms

series449.0ms

simplify108.0ms

prune352.0ms

localize14.0ms

rewrite35.0ms

series349.0ms

simplify68.0ms

prune188.0ms

localize15.0ms

rewrite30.0ms

series325.0ms

simplify65.0ms

prune244.0ms

regimes171.0ms

bsearch214.0ms

simplify1.0ms

end0.0ms

sample1.4s

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