Details

sample85.0ms

Algorithm

intervals

Results

10.0ms	206×	body	80	valid
7.0ms	26×	body	2560	valid
5.0ms	25×	body	1280	valid
3.0ms	75×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune2.0ms

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: 32.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.4b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

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

series283.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
42.0ms	(- (* b b) (* (* 3.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune252.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Merged error: 6.0b

Counts

103 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3.0 a))
1.4b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-cbrt-cube`
8×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `div-exp` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `times-frac` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `flip3--` `pow-flip` `sqrt-div` `1-exp` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `neg-log` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv` `inv-pow`

Counts

4 → 90

Calls

4 calls:

4.0ms	(/ 1 (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (* 3.0 a))
45.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	368	554
1	1514	497
2	5002	477

prune210.0ms

Filtered

102 candidates to 74 candidates (72.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	102	8	110

Merged error: 6.0b

Counts

110 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.4b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
50.0ms	(- (* b b) (* (* 3.0 a) c))
86.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune196.0ms

Filtered

92 candidates to 71 candidates (77.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	93	7	100

Merged error: 6.0b

Counts

100 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
1.4b	(- (* b b) (* 3.0 (* a c)))
1.4b	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
23.0b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-r` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* 3.0 (* a c))
4.0ms	(- (* b b) (* 3.0 (* a c)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series245.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* 3.0 (* a c))
65.0ms	(- (* b b) (* 3.0 (* a c)))
91.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
68.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	330	529
1	1217	478
2	5001	467

prune180.0ms

Filtered

92 candidates to 71 candidates (77.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	92	7	99

Merged error: 6.0b

Counts

99 → 7

regimes308.0ms

Accuracy

89.1% (3.1b remaining)

Error of 8.7b against oracle of 5.6b and baseline of 34.0b

bsearch161.0ms

Steps

Iters	Range	Point
7	6.011887282010727e+43	5.675568733030414e+45	2.9359885461337045e+45
7	2.8088005691183282e-136	8.718282365388647e-135	6.102721236610262e-136
9	-3.270551254255918e+118	-2.1334538400483563e+110	-2.4928243975796524e+116

Iters

Range

Point

6.011887282010727e+43

5.675568733030414e+45

2.9359885461337045e+45

2.8088005691183282e-136

8.718282365388647e-135

6.102721236610262e-136

-3.270551254255918e+118

-2.1334538400483563e+110

-2.4928243975796524e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	30
1	52	30
2	52	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

293.0ms	1058×	body	2560	valid
288.0ms	5895×	body	80	valid
200.0ms	872×	body	1280	valid
140.0ms	2907×	body	80	nan
84.0ms	449×	body	640	valid
36.0ms	107×	body	5120	valid
30.0ms	228×	body	320	valid
10.0ms	110×	body	160	valid

Details

sample85.0ms

simplify11.0ms

prune2.0ms

localize12.0ms

rewrite29.0ms

series283.0ms

simplify52.0ms

prune252.0ms

localize11.0ms

rewrite22.0ms

series204.0ms

simplify47.0ms

prune210.0ms

localize14.0ms

rewrite23.0ms

series225.0ms

simplify48.0ms

prune196.0ms

localize13.0ms

rewrite23.0ms

series245.0ms

simplify42.0ms

prune180.0ms

regimes308.0ms

bsearch161.0ms

simplify2.0ms

end0.0ms

sample1.3s

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