Details

sample52.0ms

Algorithm

intervals

Results

11.0ms	214×	body	80	valid
8.0ms	28×	body	2560	valid
5.0ms	19×	body	1280	valid
4.0ms	87×	body	80	nan
2.0ms	10×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	320	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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 32.9b

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))
0.7b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
24.7b	(sqrt (- (* b b) (* 4.0 (* 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 → 70

Calls

4 calls:

13.0ms	(/ (+ (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))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	394	773
1	1501	683
2	5002	673

prune149.0ms

Filtered

82 candidates to 63 candidates (23.2%)

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: 7.5b

Counts

83 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
45×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3-+` `flip-+` `div-inv`
3×	`rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 114

Calls

4 calls:

12.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
7.0ms	(+ (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))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(+ (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))))

simplify67.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	525	1585
1	2550	1372
2	5001	1305

prune151.0ms

Filtered

126 candidates to 72 candidates (42.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	126	9	135

Merged error: 7.4b

Counts

135 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

333×	`times-frac`
221×	`*-un-lft-identity`
122×	`add-sqr-sqrt`
121×	`add-cube-cbrt`
87×	`add-exp-log`
58×	`div-exp`
50×	`distribute-lft-out`
31×	`div-inv`
25×	`distribute-rgt-neg-in` `add-cbrt-cube`
21×	`associate-/r*`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
10×	`add-log-exp`
9×	`flip3-+` `flip-+`
7×	`associate-/l*`
5×	`pow1`
3×	`sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 263

Calls

4 calls:

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

series74.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(+ (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))))

simplify68.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1111	4690
1	5001	4131

prune300.0ms

Filtered

275 candidates to 118 candidates (57.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	275	9	284

Merged error: 7.4b

Counts

284 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
9.3b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `neg-log` `flip-+`

Counts

4 → 55

Calls

4 calls:

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

series51.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify132.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	243	646
1	970	537
2	4335	525
3	5003	523

prune123.0ms

Filtered

67 candidates to 54 candidates (19.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	67	9	76

Merged error: 7.4b

Counts

76 → 9

regimes408.0ms

Accuracy

86.5% (3.6b remaining)

Error of 9.6b against oracle of 6.0b and baseline of 32.5b

bsearch63.0ms

Steps

Iters	Range		Point
8	3.2772367798370246e-46	8.826811452738637e-44	5.513140388042354e-45
8	-7.483396380019031e+117	-3.515939334884751e+113	-1.0192218364023762e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

349.0ms	6480×	body	80	valid
247.0ms	824×	body	2560	valid
166.0ms	662×	body	1280	valid
135.0ms	2649×	body	80	nan
72.0ms	358×	body	640	valid
34.0ms	95×	body	5120	valid
25.0ms	162×	body	320	valid
9.0ms	89×	body	160	valid

Details

sample52.0ms

simplify12.0ms

prune4.0ms

localize11.0ms

rewrite29.0ms

series62.0ms

simplify44.0ms

prune149.0ms

localize15.0ms

rewrite30.0ms

series72.0ms

simplify67.0ms

prune151.0ms

localize14.0ms

rewrite48.0ms

series74.0ms

simplify68.0ms

prune300.0ms

localize18.0ms

rewrite16.0ms

series51.0ms

simplify132.0ms

prune123.0ms

regimes408.0ms

bsearch63.0ms

simplify2.0ms

end0.0ms

sample1.4s

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