Details

sample56.0ms

Algorithm

intervals

Results

13.0ms	181×	body	80	valid
10.0ms	36×	body	2560	valid
5.0ms	23×	body	1280	valid
4.0ms	82×	body	80	nan
3.0ms	17×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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 (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: 35.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.1b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`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-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

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

series43.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 3.0 a) c)
17.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	302	468
1	1299	428
2	5002	417

prune135.0ms

Filtered

72 candidates to 52 candidates (27.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	9	73

Merged error: 13.6b

Counts

73 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
4.3b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.8b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* b b) (* (* 3.0 a) c))
43.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
58.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	634	2580
1	3161	2341
2	5001	2328

prune315.0ms

Filtered

160 candidates to 106 candidates (33.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	154	6	160
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	156	13	169

Merged error: 13.2b

Counts

169 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
4.2b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
9.7b	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
15.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
44.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
57.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	679	1938
1	4478	1484
2	5001	1443

prune213.0ms

Filtered

122 candidates to 81 candidates (33.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	119	16	135

Merged error: 13.0b

Counts

135 → 16

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
11.5b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
25.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))
25.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
3.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
30.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
24.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	353	804
1	1351	725
2	5001	702

prune150.0ms

Filtered

63 candidates to 56 candidates (11.1%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	63	16	79

Merged error: 13.0b

Counts

79 → 16

regimes734.0ms

Accuracy

86.5% (3.1b remaining)

Error of 14.3b against oracle of 11.2b and baseline of 34.3b

bsearch108.0ms

Steps

Iters	Range		Point
9	6576192704339.47	2.9434032555578894e+20	7.7904401432269e+15
9	2.994308139190913e-109	5.986107531571838e-100	2.931974972841588e-107
9	-7.43176951740542e+107	-7.093321319689126e+100	-6.231863336282291e+107

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	56
1	60	56

end0.0ms

sample1.5s

Algorithm

intervals

Results

318.0ms	1082×	body	2560	valid
298.0ms	5839×	body	80	valid
214.0ms	903×	body	1280	valid
141.0ms	2940×	body	80	nan
81.0ms	423×	body	640	valid
40.0ms	108×	body	5120	valid
31.0ms	224×	body	320	valid
11.0ms	113×	body	160	valid

Details

sample56.0ms

simplify9.0ms

prune3.0ms

localize10.0ms

rewrite20.0ms

series43.0ms

simplify39.0ms

prune135.0ms

localize17.0ms

rewrite42.0ms

series125.0ms

simplify111.0ms

prune315.0ms

localize14.0ms

rewrite42.0ms

series124.0ms

simplify116.0ms

prune213.0ms

localize14.0ms

rewrite15.0ms

series89.0ms

simplify40.0ms

prune150.0ms

regimes734.0ms

bsearch108.0ms

simplify2.0ms

end0.0ms

sample1.5s

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