Details

sample55.0ms

Algorithm

intervals

Results

10.0ms	193×	body	80	valid
8.0ms	27×	body	2560	valid
7.0ms	29×	body	1280	valid
5.0ms	95×	body	80	nan
4.0ms	19×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	1×	body	5120	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	16
1	91	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: 33.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.2b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b	(- (* b b) (* (* 4.0 a) c))
22.1b	(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:

12.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
16.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify33.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5009	1230

prune157.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 5.2b

Counts

83 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.9b	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.2b	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.1b	(sqrt (- (* b b) (* 4.0 (* 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 → 120

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series128.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
42.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
58.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify40.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5437	2706

prune183.0ms

Filtered

84 candidates to 132 candidates (-57.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	132	9	141

Merged error: 5.1b

Counts

141 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.6b	(- (* b b) (* 4.0 (* a c)))
2.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

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

series82.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5165	1786

prune152.0ms

Filtered

71 candidates to 102 candidates (-43.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	101	10	111

Merged error: 5.0b

Counts

111 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0b	(* (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* a 2.0)))
9.2b	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

131×	`add-exp-log`
67×	`add-cbrt-cube`
64×	`prod-exp`
40×	`div-exp`
30×	`add-sqr-sqrt`
28×	`cbrt-unprod`
27×	`*-un-lft-identity`
20×	`cbrt-undiv`
17×	`times-frac`
13×	`associate-l`
11×	`add-cube-cbrt`
8×	`rec-exp` `1-exp` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `associate-r` `associate-/r*` `sqrt-prod`
4×	`flip3--` `distribute-rgt-neg-in` `associate-/r/` `flip--`
3×	`div-inv`
2×	`sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `-commutative` `associate-/l` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(* (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* a 2.0)))
12.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(* (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* a 2.0)))
56.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4965	3099
1	4965	3099

prune183.0ms

Filtered

84 candidates to 152 candidates (-81.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	152	10	162

Merged error: 5.0b

Counts

162 → 10

regimes405.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.4b

bsearch102.0ms

Steps

Iters	Range	Point
8	1.838480289737433e+68	1.744360026235418e+71	1.0729035470079235e+71
9	-6.695429941707738e-297	-7.676761036242019e-305	-7.883473021605369e-300
9	-6.247250655316605e+139	-3.660489123272618e+133	-3.8900654094429814e+133

Iters

Range

Point

1.838480289737433e+68

1.744360026235418e+71

1.0729035470079235e+71

-6.695429941707738e-297

-7.676761036242019e-305

-7.883473021605369e-300

-6.247250655316605e+139

-3.660489123272618e+133

-3.8900654094429814e+133

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	74
1	62	74

end0.0ms

sample1.6s

Algorithm

intervals

Results

315.0ms	1069×	body	2560	valid
300.0ms	5818×	body	80	valid
217.0ms	911×	body	1280	valid
142.0ms	2950×	body	80	nan
90.0ms	474×	body	640	valid
39.0ms	111×	body	5120	valid
30.0ms	216×	body	320	valid
11.0ms	116×	body	160	valid

Details

sample55.0ms

simplify3.0ms

prune8.0ms

localize11.0ms

rewrite28.0ms

series63.0ms

simplify33.0ms

prune157.0ms

localize13.0ms

rewrite46.0ms

series128.0ms

simplify40.0ms

prune183.0ms

localize13.0ms

rewrite29.0ms

series82.0ms

simplify38.0ms

prune152.0ms

localize14.0ms

rewrite49.0ms

series130.0ms

simplify69.0ms

prune183.0ms

regimes405.0ms

bsearch102.0ms

simplify1.0ms

end0.0ms

sample1.6s

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