Details

sample43.0ms

Algorithm

intervals

Results

8.0ms	34×	body	2560	valid
7.0ms	172×	body	80	valid
6.0ms	32×	body	1280	valid
3.0ms	79×	body	80	nan
2.0ms	9×	body	5120	valid
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	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

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

483×	`add-sqr-sqrt`
330×	`associate-l` `prod-diff`
309×	`*-un-lft-identity`
229×	`add-cube-cbrt`
177×	`associate-r`
125×	`unswap-sqr`
75×	`swap-sqr`
65×	`*-commutative`
60×	`times-frac`
30×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
15×	`fma-neg`
12×	`associate-/r*` `distribute-lft-out--`
10×	`fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`

Counts

4 → 541

Calls

4 calls:

44.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
31.0ms	(- (* b b) (* (* 4.0 a) c))
37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify204.0ms

Algorithm

egg-herbie

Counts

553 → 553

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1449	9181
1	4991	6678
2	5001	6678

prune698.0ms

Filtered

553 candidates to 170 candidates (30.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	544	9	553
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	545	9	554

Merged error: 6.1b

Counts

554 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

501×	`add-sqr-sqrt`
335×	`associate-l`
330×	`prod-diff`
268×	`*-un-lft-identity`
233×	`add-cube-cbrt`
217×	`associate-r`
132×	`unswap-sqr`
75×	`swap-sqr`
66×	`*-commutative`
40×	`times-frac`
36×	`frac-times` `associate-/r*`
30×	`difference-of-squares`
24×	`sqrt-prod`
23×	`add-exp-log`
20×	`flip3-+` `flip-+`
18×	`associate-*r/`
15×	`fma-neg`
13×	`add-cbrt-cube`
12×	`distribute-lft-out--`
10×	`fma-def` `prod-exp` `associate-/l*` `add-log-exp`
7×	`pow1`
5×	`distribute-rgt-neg-in`
4×	`expm1-log1p-u` `div-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `frac-2neg` `un-div-inv`
2×	`cbrt-undiv` `rec-exp` `flip3--` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `neg-log` `div-inv`

Counts

4 → 575

Calls

4 calls:

58.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
33.0ms	(- (* b b) (* (* 4.0 a) c))
34.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
48.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

587 → 587

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1758	9836
1	5001	7403

prune824.0ms

Filtered

587 candidates to 201 candidates (34.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	583	4	587
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	588	8	596

Merged error: 6.1b

Counts

596 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
0.8b	(- (* b b) (* (* 4.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

450×	`add-sqr-sqrt`
330×	`prod-diff`
312×	`associate-l`
252×	`*-un-lft-identity`
208×	`add-cube-cbrt`
159×	`associate-r`
119×	`unswap-sqr`
75×	`swap-sqr`
59×	`*-commutative`
30×	`difference-of-squares`
24×	`sqrt-prod`
15×	`times-frac` `fma-neg`
12×	`distribute-lft-out--`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 485

Calls

4 calls:

37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
32.0ms	(- (* b b) (* (* 4.0 a) c))
34.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
46.0ms	(- (* b b) (* (* 4.0 a) c))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify173.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	1263	8241
1	4050	5763
2	5001	5758

prune549.0ms

Filtered

497 candidates to 142 candidates (28.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	494	3	497
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	497	8	505

Merged error: 6.1b

Counts

505 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma b b (- (* (* (cbrt (* 4.0 a)) c) (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a))))))
1.2b	(+ (- b) (sqrt (+ (fma b b (- (* (* (cbrt (* 4.0 a)) c) (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a)))))) (* (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a))) (+ (- (* (cbrt (* 4.0 a)) c)) (* (cbrt (* 4.0 a)) c))))))
2.2b	(+ (- (* (cbrt (* 4.0 a)) c)) (* (cbrt (* 4.0 a)) c))
23.2b	(sqrt (+ (fma b b (- (* (* (cbrt (* 4.0 a)) c) (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a)))))) (* (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a))) (+ (- (* (cbrt (* 4.0 a)) c)) (* (cbrt (* 4.0 a)) c)))))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-sqr-sqrt`
160×	`associate-l`
126×	`cbrt-prod`
103×	`*-un-lft-identity`
77×	`distribute-lft-neg-in`
66×	`fma-def`
62×	`unswap-sqr`
60×	`distribute-rgt-neg-in`
49×	`add-cube-cbrt`
48×	`distribute-rgt-out`
40×	`associate-r`
37×	`distribute-lft-out`
16×	`hypot-def`
13×	`*-commutative`
12×	`add-log-exp`
7×	`neg-mul-1`
6×	`sqrt-prod`
5×	`pow1` `distribute-lft1-in`
4×	`add-exp-log` `expm1-log1p-u` `sum-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `swap-sqr` `flip-+`
2×	`+-commutative` `neg-sub0` `associate-+l-` `sqrt-div` `neg-log`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 229

Calls

4 calls:

1.0ms	(fma b b (- (* (* (cbrt (* 4.0 a)) c) (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a))))))
178.0ms	(+ (- b) (sqrt (+ (fma b b (- (* (* (cbrt (* 4.0 a)) c) (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a)))))) (* (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a))) (+ (- (* (cbrt (* 4.0 a)) c)) (* (cbrt (* 4.0 a)) c))))))
68.0ms	(+ (- (* (cbrt (* 4.0 a)) c)) (* (cbrt (* 4.0 a)) c))
173.0ms	(sqrt (+ (fma b b (- (* (* (cbrt (* 4.0 a)) c) (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a)))))) (* (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a))) (+ (- (* (cbrt (* 4.0 a)) c)) (* (cbrt (* 4.0 a)) c)))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(fma b b (- (* (* (cbrt (* 4.0 a)) c) (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a))))))
158.0ms	(+ (- b) (sqrt (+ (fma b b (- (* (* (cbrt (* 4.0 a)) c) (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a)))))) (* (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a))) (+ (- (* (cbrt (* 4.0 a)) c)) (* (cbrt (* 4.0 a)) c))))))
2.0ms	(+ (- (* (cbrt (* 4.0 a)) c)) (* (cbrt (* 4.0 a)) c))
152.0ms	(sqrt (+ (fma b b (- (* (* (cbrt (* 4.0 a)) c) (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a)))))) (* (* (cbrt (* 4.0 a)) (cbrt (* 4.0 a))) (+ (- (* (cbrt (* 4.0 a)) c)) (* (cbrt (* 4.0 a)) c)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	598	2199
1	2232	1814
2	5001	1233

prune874.0ms

Filtered

241 candidates to 171 candidates (71.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	241	8	249

Merged error: 6.1b

Counts

249 → 8

regimes240.0ms

Accuracy

85.2% (4.2b remaining)

Error of 9.7b against oracle of 5.5b and baseline of 33.8b

bsearch91.0ms

Steps

Iters	Range		Point
4	2.7062129888597453e-95	4.861630376334293e-95	3.8681552371770574e-95
9	-1.8864815038392082e+94	-1.5243980513895428e+89	-9.911609721462535e+93

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

243.0ms	1052×	body	2560	valid
241.0ms	5820×	body	80	valid
174.0ms	891×	body	1280	valid
110.0ms	2865×	body	80	nan
71.0ms	469×	body	640	valid
31.0ms	111×	body	5120	valid
27.0ms	235×	body	320	valid
9.0ms	122×	body	160	valid