Details

sample58.0ms

Algorithm

intervals

Results

11.0ms	35×	body	2560	valid
10.0ms	183×	body	80	valid
7.0ms	24×	body	1280	valid
5.0ms	91×	body	80	nan
5.0ms	23×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	1×	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

prune2.0ms

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: 32.5b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.1b	(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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune215.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 5.6b

Counts

83 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b b) (* (* 4.0 a) c))
0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.1b	(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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	481	920
1	2189	790
2	5001	777

prune214.0ms

Filtered

92 candidates to 66 candidates (71.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	93	6	99

Merged error: 5.6b

Counts

99 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.8b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3--` `flip--` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `sum-log`
1×	`+-commutative` `pow2` `neg-sub0` `associate-+l-` `flip3-+` `pow-plus` `sqrt-unprod` `neg-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 126

Calls

4 calls:

15.0ms	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
77.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	337	1382
1	1404	1213
2	5001	1175

prune283.0ms

Filtered

138 candidates to 78 candidates (56.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	138	6	144

Merged error: 5.6b

Counts

144 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
3.7b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
9.8b	(/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
116×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
45×	`associate-/l*`
40×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
21×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
10×	`neg-mul-1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `distribute-neg-frac` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
4×	`div-inv`
3×	`sqrt-prod` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sum-log` `flip--`

Counts

4 → 198

Calls

4 calls:

5.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
11.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
141.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
180.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify125.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	799	3506
1	3663	3252
2	5002	3248

prune530.0ms

Filtered

210 candidates to 159 candidates (75.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	208	8	216

Merged error: 5.5b

Counts

216 → 8

regimes180.0ms

Accuracy

90.9% (2.6b remaining)

Error of 8.3b against oracle of 5.7b and baseline of 34.3b

bsearch160.0ms

Steps

Iters	Range	Point
5	9.842021999831939e+57	2.923217818580069e+58	1.7463198609325596e+58
9	-1.1291446823308967e-280	-6.491904455839303e-286	-8.946722957732024e-284
7	-2.7078859601421552e+87	-1.2247309707199115e+86	-1.444358566469145e+87

Iters

Range

Point

9.842021999831939e+57

2.923217818580069e+58

1.7463198609325596e+58

-1.1291446823308967e-280

-6.491904455839303e-286

-8.946722957732024e-284

-2.7078859601421552e+87

-1.2247309707199115e+86

-1.444358566469145e+87

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	29
1	56	29
2	56	29

end0.0ms

sample1.2s

Algorithm

intervals

Results

243.0ms	1086×	body	2560	valid
236.0ms	5891×	body	80	valid
167.0ms	882×	body	1280	valid
111.0ms	2942×	body	80	nan
72.0ms	466×	body	640	valid
28.0ms	102×	body	5120	valid
22.0ms	204×	body	320	valid
9.0ms	116×	body	160	valid