Details

Time bar (total: 5.2s)

sample39.0ms

Algorithm
intervals
Results
14.0ms281×body80valid
4.0ms77×body80nan

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118
done16118

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.3b

localize88.0ms

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)))

rewrite65.0ms

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))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Counts
75 → 75
Iterations

Useful iterations: 3 (108.0ms)

IterNodesCost
0246646
1890606
23702588
35001584
done5001584

prune275.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.4b

localize90.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
6.2b
(/ (* a c) b)
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp
3×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*
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 74
Calls
4 calls:
20.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
32.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
12.0ms
(/ (* a c) b)
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
20.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Counts
86 → 86
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0459641
12217559
25001554
done5001554

prune308.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize93.0ms

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) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×times-frac
30×add-exp-log
26×*-un-lft-identity
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×unswap-sqr
3×associate-/r* sqrt-prod div-inv
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out
1×+-commutative neg-sub0 frac-times associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 112
Calls
4 calls:
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
149.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
108.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Counts
124 → 124
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07551328
137911149
250021095
done50021095

prune512.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.9b

localize99.0ms

Local error

Found 4 expressions with local error:

19.1b
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
19.1b
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
19.1b
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-div
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod frac-times pow1/3 associate-*r/ associate-*l/ sqrt-prod
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 51
Calls
4 calls:
21.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
22.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
24.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
90.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
90.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify78.0ms

Counts
63 → 63
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0227588
1714532
22768486
35001485
done5001485

prune366.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.9b

regimes146.0ms

Accuracy

94.7% (0.8b remaining)

Error of 7.7b against oracle of 6.9b and baseline of 21.9b

bsearch267.0ms

Steps
ItersRangePoint
5
3.355600980676121e+98
1.2784432988208537e+99
1.0367289971530488e+99
11
-5.294604476916941e-305
2.889381232659679e-274
6.40122866550584e-310
10
-9.407223570539366e+155
-5.3767202001825486e+144
-1.3292983864514407e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07296
17296
done7296

end0.0ms

sample881.0ms

Algorithm
intervals
Results
433.0ms8707×body80valid
123.0ms2850×body80nan