Details

sample51.0ms

Algorithm

intervals

Results

10.0ms	187×	body	80	valid
10.0ms	33×	body	2560	valid
8.0ms	32×	body	1280	valid
5.0ms	95×	body	80	nan
2.0ms	9×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	4×	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

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: 35.6b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0b	(sqrt (- (* b b) (* (* 4.0 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-/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))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5002	673

prune204.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 6.3b

Counts

83 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.5b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
228.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
277.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	646	2693
1	3163	2447
2	5003	2434

prune384.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	167	9	176

Merged error: 6.3b

Counts

176 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
0.9b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.6b	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
25.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`flip3--` `sqrt-prod` `flip--`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 72

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
263.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify93.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	486	952
1	2894	749
2	5002	741

prune209.0ms

Filtered

84 candidates to 58 candidates (69.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	84	9	93

Merged error: 6.3b

Counts

93 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
0.8b	(- (* b b) (* (* 4.0 a) c))
0.9b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`add-log-exp`
7×	`div-exp` `associate-/r*`
5×	`pow1` `cbrt-undiv` `div-inv`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `prod-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `neg-log` `clear-num` `associate-/r/` `cbrt-unprod`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 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)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
47.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	549	1186
1	2337	1074
2	5002	1074

prune247.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	107	8	115

Merged error: 6.3b

Counts

115 → 8

regimes204.0ms

Accuracy

91.6% (2.1b remaining)

Error of 7.5b against oracle of 5.4b and baseline of 30.9b

bsearch201.0ms

Steps

Iters	Range	Point
9	1.554603894687908e+31	4.1009785056144894e+37	3.345560952441054e+37
9	2.4464025933335693e-149	1.07121093016595e-142	2.4885130106027322e-149
7	-3.119450221310465e+111	-1.7054991696093843e+109	-8.449278771600537e+109

Iters

Range

Point

1.554603894687908e+31

4.1009785056144894e+37

3.345560952441054e+37

2.4464025933335693e-149

1.07121093016595e-142

2.4885130106027322e-149

-3.119450221310465e+111

-1.7054991696093843e+109

-8.449278771600537e+109

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	30
1	53	30
2	53	30

end0.0ms

sample1.4s

Algorithm

intervals

Results

303.0ms	1035×	body	2560	valid
297.0ms	5868×	body	80	valid
214.0ms	907×	body	1280	valid
143.0ms	2895×	body	80	nan
84.0ms	457×	body	640	valid
40.0ms	117×	body	5120	valid
32.0ms	232×	body	320	valid
12.0ms	125×	body	160	valid

Details

sample51.0ms

simplify11.0ms

prune3.0ms

localize15.0ms

rewrite27.0ms

series333.0ms

simplify44.0ms

prune204.0ms

localize18.0ms

rewrite47.0ms

series653.0ms

simplify108.0ms

prune384.0ms

localize16.0ms

rewrite34.0ms

series452.0ms

simplify93.0ms

prune209.0ms

localize14.0ms

rewrite30.0ms

series359.0ms

simplify81.0ms

prune247.0ms

regimes204.0ms

bsearch201.0ms

simplify2.0ms

end0.0ms

sample1.4s

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