Details

sample58.0ms

Algorithm

intervals

Results

13.0ms	34×	body	2560	valid
11.0ms	194×	body	80	valid
8.0ms	29×	body	1280	valid
5.0ms	92×	body	80	nan
3.0ms	13×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify11.0ms

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

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: 32.1b

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))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.0b	(+ (neg b) (sqrt (- (* 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))
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)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms	(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	405	779
1	1563	685
2	5001	674

prune199.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 6.0b

Counts

83 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.0b	(+ (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

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

15.0ms	(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
45.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	481	920
1	2189	790
2	5001	777

prune202.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Merged error: 6.0b

Counts

101 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

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:

13.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(- (* 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)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	525	1586
1	2570	1373
2	5001	1306

prune230.0ms

Filtered

126 candidates to 71 candidates (56.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	127	7	134

Merged error: 5.9b

Counts

134 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.8b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3--` `flip--` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `sum-log`
1×	`+-commutative` `pow2` `neg-sub0` `associate-+l-` `flip3-+` `pow-plus` `sqrt-unprod` `neg-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 126

Calls

4 calls:

15.0ms	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* 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))))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
75.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	337	1382
1	1404	1213
2	5001	1175

prune305.0ms

Filtered

138 candidates to 78 candidates (56.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	138	7	145

Merged error: 5.9b

Counts

145 → 7

regimes179.0ms

Accuracy

89.9% (3.0b remaining)

Error of 8.3b against oracle of 5.3b and baseline of 34.6b

bsearch186.0ms

Steps

Iters	Range	Point
8	1.3889487570498298e+76	5.0983209320788285e+78	4.404095572199115e+76
6	8.311617275315721e-208	1.2391898617977871e-206	1.3799070328184513e-207
9	-4.225393322780344e+106	-5.495421239091533e+98	-3.944298534745975e+106

Iters

Range

Point

1.3889487570498298e+76

5.0983209320788285e+78

4.404095572199115e+76

8.311617275315721e-208

1.2391898617977871e-206

1.3799070328184513e-207

-4.225393322780344e+106

-5.495421239091533e+98

-3.944298534745975e+106

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	32
1	53	32

end0.0ms

sample1.5s

Algorithm

intervals

Results

351.0ms	1178×	body	2560	valid
301.0ms	5750×	body	80	valid
219.0ms	912×	body	1280	valid
159.0ms	2942×	body	80	nan
90.0ms	450×	body	640	valid
40.0ms	102×	body	5120	valid
34.0ms	233×	body	320	valid
10.0ms	109×	body	160	valid

Details

sample58.0ms

simplify11.0ms

prune2.0ms

localize11.0ms

rewrite28.0ms

series286.0ms

simplify45.0ms

prune199.0ms

localize12.0ms

rewrite35.0ms

series312.0ms

simplify62.0ms

prune202.0ms

localize12.0ms

rewrite33.0ms

series339.0ms

simplify101.0ms

prune230.0ms

localize27.0ms

rewrite36.0ms

series275.0ms

simplify64.0ms

prune305.0ms

regimes179.0ms

bsearch186.0ms

simplify2.0ms

end0.0ms

sample1.5s

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