Details

Time bar (total: 40.4s)

sample56.0ms

Algorithm
intervals
Results
12.0ms156×body160valid
10.0ms514×pre80true
9.0ms258×body80nan
5.0ms47×body320valid
2.0ms53×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune6.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 45.6b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
116×*-un-lft-identity
60×times-frac
42×unswap-sqr
36×add-cube-cbrt associate-*l*
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
18×associate-*r*
14×distribute-rgt-neg-in
12×associate-/r* *-commutative distribute-lft-out--
10×add-log-exp
9×add-exp-log add-cbrt-cube
6×swap-sqr
5×pow1 associate-/l*
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 cbrt-unprod div-inv
Counts
4 → 178
Calls
4 calls:
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series347.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
54.0ms
(- (* b b) (* (* 4.0 a) c))
120.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
91.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06212253
124432157
250022140

prune264.0ms

Filtered
190 candidates to 109 candidates (42.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1864190
Fresh000
Picked101
Done000
Total1874191

Merged error: 0.1b

Counts
191 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite346.0ms

Algorithm
rewrite-expression-head
Rules
1801×*-un-lft-identity
1346×times-frac
946×add-sqr-sqrt
408×distribute-lft-out--
400×distribute-lft-out
385×add-cube-cbrt
377×associate-*l*
217×difference-of-squares
168×associate-*r*
101×distribute-rgt-neg-in sqrt-prod
74×unswap-sqr
69×associate-/l*
59×*-commutative
28×associate-/r/
26×associate-/r*
23×associate-/l/
18×add-exp-log add-cbrt-cube
16×flip3-- flip--
15×div-inv
10×add-log-exp
7×cbrt-undiv div-exp
4×pow1
3×frac-2neg diff-log div-sub swap-sqr clear-num
2×associate-+l- sub-neg flip3-+ prod-exp cbrt-unprod flip-+
1×associate--l- neg-sub0 neg-log
Counts
4 → 896
Calls
4 calls:
40.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(- (* b b) (* (* 4.0 a) c))
114.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
88.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series609.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
53.0ms
(- (* b b) (* (* 4.0 a) c))
280.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
188.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify241.0ms

Algorithm
egg-herbie
Counts
908 → 908
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
0173224064
1500122943

prune1.1s

Filtered
908 candidates to 284 candidates (68.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New9026908
Fresh213
Picked101
Done000
Total9057912

Merged error: 0b

Counts
912 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (* (* (sqrt 4.0) (sqrt a)) (sqrt c)) b) (- b (* (* (sqrt 4.0) (sqrt a)) (sqrt c))))))) (* 2.0 a))
0.3b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (* (* (sqrt 4.0) (sqrt a)) (sqrt c)) b) (- b (* (* (sqrt 4.0) (sqrt a)) (sqrt c)))))))
0.4b
(* (* (sqrt 4.0) (sqrt a)) (sqrt c))
0.4b
(* (* (sqrt 4.0) (sqrt a)) (sqrt c))

rewrite389.0ms

Algorithm
rewrite-expression-head
Rules
1974×*-un-lft-identity
1528×times-frac
1332×add-sqr-sqrt
471×associate-*l*
456×distribute-lft-out
434×add-cube-cbrt
428×distribute-lft-out--
300×difference-of-squares
252×sqrt-prod
213×associate-*r*
207×unswap-sqr
100×distribute-rgt-neg-in
76×associate-/l*
67×*-commutative
28×add-exp-log associate-/r* associate-/r/ add-cbrt-cube
24×associate-/l/
20×pow1
15×div-inv
14×flip3-- pow-prod-down flip--
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×sqrt-pow1 pow1/2
4×sqrt-unprod add-log-exp
3×frac-2neg div-sub clear-num
2×associate-+l- flip3-+ flip-+
Counts
4 → 1053
Calls
4 calls:
140.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (* (* (sqrt 4.0) (sqrt a)) (sqrt c)) b) (- b (* (* (sqrt 4.0) (sqrt a)) (sqrt c))))))) (* 2.0 a))
115.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (* (* (sqrt 4.0) (sqrt a)) (sqrt c)) b) (- b (* (* (sqrt 4.0) (sqrt a)) (sqrt c)))))))
14.0ms
(* (* (sqrt 4.0) (sqrt a)) (sqrt c))
14.0ms
(* (* (sqrt 4.0) (sqrt a)) (sqrt c))

series1.9s

Counts
4 → 12
Calls
4 calls:
702.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (* (* (sqrt 4.0) (sqrt a)) (sqrt c)) b) (- b (* (* (sqrt 4.0) (sqrt a)) (sqrt c))))))) (* 2.0 a))
804.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (* (* (sqrt 4.0) (sqrt a)) (sqrt c)) b) (- b (* (* (sqrt 4.0) (sqrt a)) (sqrt c)))))))
178.0ms
(* (* (sqrt 4.0) (sqrt a)) (sqrt c))
179.0ms
(* (* (sqrt 4.0) (sqrt a)) (sqrt c))

simplify364.0ms

Algorithm
egg-herbie
Counts
1065 → 1065
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0208642288
1500241623

prune1.9s

Filtered
1065 candidates to 364 candidates (65.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New106411065
Fresh246
Picked011
Done000
Total106661072

Merged error: 0b

Counts
1072 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ 1 1) (/ (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 4.0 (* a c))))
0.3b
(/ (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 4.0 (* a c)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
21261×times-frac
14135×add-sqr-sqrt
9210×associate-*r*
9027×*-un-lft-identity
7683×add-cube-cbrt
7356×associate-*l*
2918×unswap-sqr
1453×*-commutative
681×difference-of-squares
672×distribute-lft-out--
623×associate-/r*
593×div-inv
364×add-exp-log
333×distribute-rgt-neg-in sqrt-prod
182×div-exp
149×add-cbrt-cube
147×prod-exp
68×associate-/l*
57×cbrt-undiv cbrt-unprod
53×associate-/r/
50×1-exp
20×rec-exp
13×associate-/l/
9×pow1
6×associate-*r/ add-log-exp
4×flip3-- frac-2neg clear-num flip--
3×sub-neg swap-sqr pow-prod-down
2×distribute-rgt-in distribute-lft-in
1×diff-log
Counts
4 → 8963
Calls
4 calls:
23.0ms
(- (* b b) (* (* 4.0 a) c))
246.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
294.0ms
(/ (/ 1 1) (/ (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 4.0 (* a c))))
74.0ms
(/ (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 4.0 (* a c)))

series487.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* (* 4.0 a) c))
117.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
178.0ms
(/ (/ 1 1) (/ (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 4.0 (* a c))))
140.0ms
(/ (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 4.0 (* a c)))

simplify2.2s

Algorithm
egg-herbie
Counts
8975 → 8975
Iterations

Useful iterations: 0 (119.0ms)

IterNodesCost
09965230860

prune26.5s

Filtered
8975 candidates to 6227 candidates (30.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New897418975
Fresh134
Picked101
Done011
Total897658981

Merged error: 0b

Counts
8981 → 5

regimes93.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03325
13325

end0.0ms

sample1.6s

Algorithm
intervals
Results
361.0ms4807×body160valid
311.0ms16272×pre80true
306.0ms8272×body80nan
156.0ms1402×body320valid
67.0ms1791×body80valid