Details

sample57.0ms

Algorithm

intervals

Results

14.0ms	181×	body	80	valid
11.0ms	38×	body	2560	valid
4.0ms	92×	body	80	nan
4.0ms	16×	body	1280	valid
3.0ms	14×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	7×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	128	17
1	128	17

prune7.0ms

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: 33.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.4b	(- (* b b) (* 4.0 (* a c)))
2.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

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:

11.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5035	1467

prune169.0ms

Filtered

64 candidates to 89 candidates (-39.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	11	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	11	90

Merged error: 5.1b

Counts

90 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
3.9b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.5b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
77×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
20×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
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 → 138

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4955	3663
1	4955	3663

prune272.0ms

Filtered

108 candidates to 150 candidates (-38.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	149	12	161

Merged error: 5.1b

Counts

161 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
13.2b	(* (/ a 4.0) (/ 2.0 (* a c)))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

6.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(* (/ a 4.0) (/ 2.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
2.0ms	(* (/ a 4.0) (/ 2.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4992	1073
1	4992	1073

prune164.0ms

Filtered

72 candidates to 100 candidates (-38.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	101	11	112

Merged error: 5.1b

Counts

112 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 0.5 c)))
1.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

12.0ms	(/ 1 (* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 0.5 c)))
6.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 0.5 c)))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4970	1330
1	4970	1330

prune102.0ms

Filtered

59 candidates to 91 candidates (-54.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	91	11	102

Merged error: 5.1b

Counts

102 → 11

regimes285.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.9b

bsearch104.0ms

Steps

Iters	Range	Point
8	1.838480289737433e+68	1.744360026235418e+71	7.321363481201363e+70
8	-7.676761036242019e-305	3.179664591143469e-308	-3.164722136195457e-309
9	-6.247250655316605e+139	-3.660489123272618e+133	-1.7820655524002302e+138

Iters

Range

Point

1.838480289737433e+68

1.744360026235418e+71

7.321363481201363e+70

-7.676761036242019e-305

3.179664591143469e-308

-3.164722136195457e-309

-6.247250655316605e+139

-3.660489123272618e+133

-1.7820655524002302e+138

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	65
1	46	65

end0.0ms

sample1.6s

Algorithm

intervals

Results

318.0ms	1046×	body	2560	valid
301.0ms	5873×	body	80	valid
215.0ms	872×	body	1280	valid
143.0ms	2946×	body	80	nan
93.0ms	465×	body	640	valid
35.0ms	98×	body	5120	valid
34.0ms	225×	body	320	valid
12.0ms	121×	body	160	valid

Details

sample57.0ms

simplify4.0ms

prune7.0ms

localize11.0ms

rewrite28.0ms

series59.0ms

simplify41.0ms

prune169.0ms

localize13.0ms

rewrite40.0ms

series125.0ms

simplify57.0ms

prune272.0ms

localize14.0ms

rewrite25.0ms

series40.0ms

simplify44.0ms

prune164.0ms

localize12.0ms

rewrite27.0ms

series64.0ms

simplify73.0ms

prune102.0ms

regimes285.0ms

bsearch104.0ms

simplify1.0ms

end0.0ms

sample1.6s

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