Details

Time bar (total: 17.1s)

sample58.0ms

Algorithm
intervals
Results
13.0ms175×body160valid
11.0ms549×pre80true
10.0ms293×body80nan
4.0ms39×body320valid
2.0ms42×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 46.2b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite131.0ms

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:
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(- (* b b) (* (* 4.0 a) c))
40.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series329.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
118.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify81.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06212253
124432157
250022140

prune258.0ms

Filtered
190 candidates to 109 candidates (57.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1873190
Fresh000
Picked101
Done000
Total1883191

Merged error: 0.2b

Counts
191 → 3

localize19.0ms

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))
0.3b
(/ (/ (+ (- (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)))))

rewrite345.0ms

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:
33.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
84.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series594.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
135.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
326.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify247.0ms

Algorithm
egg-herbie
Counts
908 → 908
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0173224064
1500122943

prune1.1s

Filtered
908 candidates to 285 candidates (31.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New9008908
Fresh112
Picked101
Done000
Total9029911

Merged error: 0b

Counts
911 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a)
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(* (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
1282×*-un-lft-identity
822×associate-/l*
799×add-sqr-sqrt
690×frac-times
557×times-frac
418×add-cube-cbrt
311×associate-/r*
307×associate-/l/
268×distribute-lft-out--
216×distribute-lft-out
169×difference-of-squares
142×associate-*l*
85×associate-*r*
83×clear-num
81×frac-2neg
77×distribute-rgt-neg-in sqrt-prod
48×flip3-+ flip-+
46×associate-*r/
45×add-exp-log
40×associate-/r/
29×add-cbrt-cube
26×unswap-sqr
24×div-inv
21×flip3-- flip--
20×div-exp
15×associate-*l/
11×cbrt-undiv
10×prod-exp
7×pow1
6×un-div-inv cbrt-unprod add-log-exp
4×*-commutative
3×rec-exp 1-exp swap-sqr
1×associate-+l- sub-neg pow-flip diff-log div-sub pow-prod-down inv-pow
Counts
4 → 1028
Calls
4 calls:
37.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
48.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a)
25.0ms
(- (* b b) (* (* 4.0 a) c))
146.0ms
(* (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

series302.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a)
50.0ms
(- (* b b) (* (* 4.0 a) c))
133.0ms
(* (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

simplify277.0ms

Algorithm
egg-herbie
Counts
1040 → 1040
Iterations

Useful iterations: 1 (68.0ms)

IterNodesCost
0317024151
1500121715

prune1.4s

Filtered
1040 candidates to 352 candidates (33.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New103731040
Fresh448
Picked011
Done000
Total104181049

Merged error: 0b

Counts
1049 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))
0.3b
(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
0.4b
(* (/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))) (/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0))
41.1b
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
9189×*-un-lft-identity
3810×distribute-lft-out
3729×associate-*l*
2842×add-sqr-sqrt
2819×times-frac
2694×associate-/l*
2088×frac-times
1203×unpow-prod-down
1182×add-cube-cbrt
1077×difference-of-squares
1048×associate-/r*
996×distribute-rgt-neg-in
908×distribute-lft-out--
710×associate-/l/
589×sqr-pow
469×sqrt-prod
339×pow-unpow
336×difference-cubes
294×associate-*r*
135×clear-num
134×frac-2neg
123×distribute-rgt-out
101×flip3-+ flip-+
90×unswap-sqr
81×div-inv
69×associate-*l/
52×associate-*r/
40×sqrt-div
31×add-exp-log add-cbrt-cube
28×*-commutative
23×un-div-inv
22×flip3-- flip--
16×frac-add
15×swap-sqr
12×cbrt-undiv div-exp
8×pow1
6×prod-exp cbrt-unprod add-log-exp
4×associate-/r/
3×pow-pow
2×distribute-lft-neg-out div-sub
1×+-commutative pow-to-exp associate-+l- sqrt-pow1 pow1/2 unpow3 unsub-neg pow-prod-down pow-exp sum-log sqrt-pow2 rem-cube-cbrt
Counts
4 → 3694
Calls
4 calls:
112.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))
23.0ms
(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
1.1s
(* (/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))) (/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0))
293.0ms
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series722.0ms

Counts
4 → 12
Calls
4 calls:
232.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))
49.0ms
(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
309.0ms
(* (/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))) (/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0))
133.0ms
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.6s

Algorithm
egg-herbie
Counts
3706 → 3706
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
05002150181

prune5.6s

Filtered
3706 candidates to 902 candidates (24.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New370423706
Fresh246
Picked101
Done011
Total370773714

Merged error: 0b

Counts
3714 → 7

regimes131.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03117
13117

end0.0ms

sample1.5s

Algorithm
intervals
Results
354.0ms4820×body160valid
323.0ms16270×pre80true
290.0ms8270×body80nan
153.0ms1386×body320valid
68.0ms1794×body80valid