Details

sample55.0ms

Algorithm

intervals

Results

14.0ms	48×	body	2560	valid
9.0ms	175×	body	80	valid
5.0ms	21×	body	1280	valid
4.0ms	84×	body	80	nan
4.0ms	20×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	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: 34.8b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

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)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
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))))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune150.0ms

Filtered

89 candidates to 65 candidates (27.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Merged error: 5.0b

Counts

90 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

14.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
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))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
10.0ms	(- (* 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))))

simplify58.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	463	989
1	2033	868
2	5001	860

prune131.0ms

Filtered

97 candidates to 64 candidates (34.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	96	8	104

Merged error: 5.0b

Counts

104 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
5.7b	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
9.9b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
52×	`times-frac`
51×	`add-exp-log`
30×	`add-cube-cbrt` `associate-l`
27×	`add-cbrt-cube`
20×	`prod-exp`
18×	`difference-of-squares`
16×	`div-exp`
13×	`distribute-lft-out`
12×	`sqrt-prod`
9×	`distribute-lft-out--`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `associate-r`
6×	`associate-/r*` `add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `associate-/l*`
3×	`div-inv`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 149

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
11.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series128.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
46.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
59.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify117.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	758	2360
1	3752	2016
2	5001	1993

prune248.0ms

Filtered

161 candidates to 102 candidates (36.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	160	9	169

Merged error: 4.9b

Counts

169 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.8b	(- (* b b) (* 4.0 (* a c)))
14.6b	(/ (* 4.0 (* a c)) (* 2.0 a))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

6.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	399	576
1	2207	498
2	5002	498

prune89.0ms

Filtered

79 candidates to 54 candidates (31.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	4	5
Picked	1	0	1
Done	0	3	3
Total	80	8	88

Merged error: 4.9b

Counts

88 → 8

regimes335.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.3b against oracle of 5.5b and baseline of 29.3b

bsearch103.0ms

Steps

Iters	Range	Point
9	3.740966656805541e+90	2.271321644956683e+99	1.8862236256436264e+99
10	-6.101116520471646e-307	2.9396268789097114e-297	1.6112937870416748e-307
8	-1.795609024723082e+157	-2.0984588557191883e+153	-3.1668736300451263e+153

Iters

Range

Point

3.740966656805541e+90

2.271321644956683e+99

1.8862236256436264e+99

-6.101116520471646e-307

2.9396268789097114e-297

1.6112937870416748e-307

-1.795609024723082e+157

-2.0984588557191883e+153

-3.1668736300451263e+153

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	23
1	39	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

316.0ms	1068×	body	2560	valid
299.0ms	5890×	body	80	valid
214.0ms	904×	body	1280	valid
137.0ms	2788×	body	80	nan
83.0ms	425×	body	640	valid
43.0ms	121×	body	5120	valid
29.0ms	210×	body	320	valid
11.0ms	112×	body	160	valid

Details

sample55.0ms

simplify12.0ms

prune3.0ms

localize15.0ms

rewrite27.0ms

series58.0ms

simplify43.0ms

prune150.0ms

localize13.0ms

rewrite31.0ms

series58.0ms

simplify58.0ms

prune131.0ms

localize18.0ms

rewrite43.0ms

series128.0ms

simplify117.0ms

prune248.0ms

localize14.0ms

rewrite22.0ms

series39.0ms

simplify55.0ms

prune89.0ms

regimes335.0ms

bsearch103.0ms

simplify1.0ms

end0.0ms

sample1.5s

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