Details

sample55.0ms

Algorithm

intervals

Results

13.0ms	200×	body	80	valid
9.0ms	30×	body	2560	valid
7.0ms	31×	body	1280	valid
4.0ms	85×	body	80	nan
3.0ms	15×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	3×	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	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune4.0ms

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: 32.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.7b	(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))
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))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	394	773
1	1501	683
2	5002	673

prune139.0ms

Filtered

82 candidates to 63 candidates (23.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 5.1b

Counts

83 → 5

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)))
0.6b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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:

16.0ms	(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
14.0ms	(+ (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))))

simplify56.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	470	914
1	2126	788
2	5001	776

prune124.0ms

Filtered

92 candidates to 65 candidates (29.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	91	6	97

Merged error: 5.1b

Counts

97 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.5b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.1b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

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))
11.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
55.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	635	2693
1	2974	2447
2	5001	2434

prune248.0ms

Filtered

166 candidates to 111 candidates (33.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	165	7	172

Merged error: 5.0b

Counts

172 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0b	(/ (* 2.0 a) (* 4.0 (* a c)))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

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×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `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 → 70

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series42.0ms

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)))))
2.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	410	626
1	2230	543
2	5001	535

prune95.0ms

Filtered

82 candidates to 55 candidates (32.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	2	3
Picked	1	0	1
Done	0	3	3
Total	83	6	89

Merged error: 5.0b

Counts

89 → 6

regimes314.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.4b

bsearch83.0ms

Steps

Iters	Range	Point
6	3.740966656805541e+90	3.763859088204499e+91	2.1173930570711685e+91
8	-2.450180232760445e-303	-6.101116520471646e-307	-7.878728067861033e-306
9	-3.6502939682616286e+159	-2.0984588557191883e+153	-2.336606735933724e+153

Iters

Range

Point

3.740966656805541e+90

3.763859088204499e+91

2.1173930570711685e+91

-2.450180232760445e-303

-6.101116520471646e-307

-7.878728067861033e-306

-3.6502939682616286e+159

-2.0984588557191883e+153

-2.336606735933724e+153

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	25
1	45	25

end0.0ms

sample1.5s

Algorithm

intervals

Results

306.0ms	1043×	body	2560	valid
298.0ms	5859×	body	80	valid
223.0ms	919×	body	1280	valid
139.0ms	2796×	body	80	nan
90.0ms	485×	body	640	valid
40.0ms	113×	body	5120	valid
33.0ms	237×	body	320	valid
9.0ms	98×	body	160	valid

Details

sample55.0ms

simplify9.0ms

prune4.0ms

localize12.0ms

rewrite27.0ms

series64.0ms

simplify46.0ms

prune139.0ms

localize13.0ms

rewrite31.0ms

series60.0ms

simplify56.0ms

prune124.0ms

localize13.0ms

rewrite46.0ms

series127.0ms

simplify97.0ms

prune248.0ms

localize14.0ms

rewrite25.0ms

series42.0ms

simplify58.0ms

prune95.0ms

regimes314.0ms

bsearch83.0ms

simplify1.0ms

end0.0ms

sample1.5s

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