Details

Time bar (total: 5.4s)

sample38.0ms

Algorithm
intervals
Results
15.0ms281×body80valid
4.0ms77×body80nan

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118
done16118

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.3b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Counts
75 → 75
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
0246646
1890606
23702588
35001584
done5001584

prune283.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.4b

localize91.0ms

Local error

Found 4 expressions with local error:

5.4b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.7b
(cbrt (- (* b b) (* (* 4.0 a) c)))
25.7b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log cbrt-div flip3-- add-cbrt-cube flip--
3×sqrt-prod
2×pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 55
Calls
4 calls:
12.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
104.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Counts
67 → 67
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0363836
11402760
25001731
done5001731

prune367.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.4b

localize94.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.2b
(/ (* a c) b)
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
8×add-log-exp
5×pow1
4×cbrt-undiv div-exp distribute-lft-out--
3×distribute-rgt-neg-in sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l* difference-of-squares
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 80
Calls
4 calls:
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
37.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
10.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
179.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
21.0ms
(/ (* a c) b)
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0454718
12113629
25001621
done5001621

prune346.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.9b

localize98.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.0b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×*-un-lft-identity times-frac
30×add-exp-log
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×associate-/r* unswap-sqr
4×distribute-lft-out--
3×distribute-rgt-neg-in sqrt-prod div-inv
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out difference-of-squares
1×+-commutative neg-sub0 frac-times associate-+l- rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 118
Calls
4 calls:
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
36.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
211.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify125.0ms

Counts
130 → 130
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
07511431
136801244
250011199
done50011199

prune562.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

regimes204.0ms

Accuracy

93.3% (0.9b remaining)

Error of 7.8b against oracle of 6.9b and baseline of 20.7b

bsearch164.0ms

Steps
ItersRangePoint
5
3.355600980676121e+98
1.2784432988208537e+99
1.1125484838729303e+99
10
-9.407223570539366e+155
-5.3767202001825486e+144
-1.3292983864514407e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06567
16567
done6567

end0.0ms

sample952.0ms

Algorithm
intervals
Results
458.0ms8707×body80valid
145.0ms2850×body80nan