Details

sample53.0ms

Algorithm

intervals

Results

22.0ms	276×	body	80	valid
7.0ms	98×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	79	18
2	136	18
3	161	18
4	173	18
5	177	18
6	177	18

prune5.0ms

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: 22.7b

Counts

2 → 1

localize142.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 60

Calls

4 calls:

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

series51.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (neg b) (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)))

simplify122.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	223	579
1	875	551
2	3958	543
3	5001	540

prune402.0ms

Filtered

72 candidates to 55 candidates (23.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	7	73

Merged error: 7.9b

Counts

73 → 7

localize144.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
4.5b	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
5.8b	(/ (* a c) b)
26.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-sub`

Counts

4 → 72

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
4.0ms	(/ (* a c) b)
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
5.0ms	(/ (* a c) b)
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	423	596
1	1940	520
2	5002	518

prune560.0ms

Filtered

84 candidates to 61 candidates (27.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 5.8b

Counts

91 → 10

localize143.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b	(- (* b b) (* (* 4.0 a) c))
26.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

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:

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

series90.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(+ (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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	375	757
1	1596	658
2	5001	645

prune479.0ms

Filtered

81 candidates to 61 candidates (24.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 5.8b

Counts

91 → 10

localize142.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2.0 (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
0.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b	(- (* b b) (* (* 4.0 a) c))
26.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
113×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
61×	`add-cube-cbrt`
26×	`distribute-lft-out`
19×	`associate-/r*`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `div-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `neg-log` `clear-num` `associate-/r/` `flip-+`

Counts

4 → 136

Calls

4 calls:

16.0ms	(/ 2.0 (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 2.0 (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	588	1909
1	2460	1816
2	5001	1810

prune1.1s

Filtered

148 candidates to 102 candidates (31.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	149	9	158

Merged error: 5.6b

Counts

158 → 9

regimes318.0ms

Accuracy

91.6% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 21.4b

bsearch116.0ms

Steps

Iters	Range		Point
4	3.1466272044128187e+123	6.05509838734878e+123	4.330289328360896e+123
6	-4.4427042201329086e+164	-7.317214014952993e+163	-7.436798123151509e+163

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	45
1	46	45

end0.0ms

sample1.1s

Algorithm

intervals

Results

566.0ms	8731×	body	80	valid
176.0ms	2913×	body	80	nan

Details

sample53.0ms

simplify13.0ms

prune5.0ms

localize142.0ms

rewrite20.0ms

series51.0ms

simplify122.0ms

prune402.0ms

localize144.0ms

rewrite22.0ms

series40.0ms

simplify52.0ms

prune560.0ms

localize143.0ms

rewrite31.0ms

series90.0ms

simplify43.0ms

prune479.0ms

localize142.0ms

rewrite37.0ms

series67.0ms

simplify69.0ms

prune1.1s

regimes318.0ms

bsearch116.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling