Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	206×	body	80	valid
7.0ms	32×	body	2560	valid
4.0ms	23×	body	1280	valid
4.0ms	103×	body	80	nan
3.0ms	19×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune3.0ms

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: 33.7b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite33.0ms

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:

16.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
48.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune203.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 6.1b

Counts

83 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

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-/r*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

11.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
7.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	368	755
1	1544	656
2	5002	644

prune178.0ms

Filtered

81 candidates to 61 candidates (75.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	78	11	89

Merged error: 6.1b

Counts

89 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite32.0ms

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

series343.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	477	921
1	2173	791
2	5001	778

prune219.0ms

Filtered

92 candidates to 66 candidates (71.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	89	14	103

Merged error: 6.1b

Counts

103 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

21.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
7.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms	(- (* b b) (* (* 3.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	612	1234
1	2986	1078
2	5001	1068

prune237.0ms

Filtered

116 candidates to 80 candidates (69.0%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	116	14	130

Merged error: 6.1b

Counts

130 → 14

regimes472.0ms

Accuracy

82.9% (4.9b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 33.9b

bsearch110.0ms

Steps

Iters	Range		Point
10	2.319058093766752e-122	4.8666627780759835e-109	2.86122009180682e-109
8	-7.85932808106197e+156	-9.798525195327539e+152	-1.0010895938656462e+153

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

233.0ms	1056×	body	2560	valid
210.0ms	5771×	body	80	valid
169.0ms	954×	body	1280	valid
101.0ms	2946×	body	80	nan
64.0ms	482×	body	640	valid
30.0ms	114×	body	5120	valid
23.0ms	227×	body	320	valid
8.0ms	110×	body	160	valid