Details

Time bar (total: 11.8s)

sample40.0ms

Algorithm
intervals
Results
8.0ms201×body80valid
7.0ms27×body2560valid
6.0ms35×body1280valid
3.0ms87×body80nan
2.0ms12×body640valid
1.0ms7×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify79.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26317
311417
413117
513717
614017
done14017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
36.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify446.0ms

Counts
89 → 89
Iterations

Useful iterations: done (443.0ms)

IterNodesCost
01571750
14121650
213881474
done50001465

prune265.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.3b
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
58×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
22×difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 141
Calls
4 calls:
18.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
51.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
32.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series432.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
115.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
157.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify966.0ms

Counts
153 → 153
Iterations

Useful iterations: done (960.0ms)

IterNodesCost
02505241
16364740
223304054
done50004052

prune450.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

2.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
6.7b
(/ (+ 0 (* 4.0 (* a c))) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
594×times-frac
526×add-sqr-sqrt
482×sqrt-prod
388×*-un-lft-identity
252×add-cube-cbrt
136×difference-of-squares
68×distribute-lft-out--
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-- flip--
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×flip3-+ flip-+
Counts
4 → 441
Calls
4 calls:
70.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
30.0ms
(/ (+ 0 (* 4.0 (* a c))) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series919.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
554.0ms
(/ (+ 0 (* 4.0 (* a c))) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts
453 → 453
Iterations

Useful iterations: done (2.1s)

IterNodesCost
044727116
1104523354
2396121863
done500021860

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

localize24.0ms

Local error

Found 4 expressions with local error:

4.8b
(* (/ 1 (* (cbrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (cbrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))) (/ (* 4.0 a) (/ (cbrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
155×add-exp-log
64×prod-exp
63×times-frac
62×div-exp
57×add-cbrt-cube
46×add-sqr-sqrt
36×associate-*r*
33×*-un-lft-identity
28×cbrt-undiv
26×add-cube-cbrt cbrt-unprod
18×cbrt-prod
15×associate-*l*
12×cbrt-div sqrt-prod
10×rec-exp 1-exp
9×pow1 flip3-- associate-/r/ flip--
6×sqrt-div difference-of-squares
5×frac-times
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*l/ div-inv distribute-lft-out-- unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 161
Calls
4 calls:
253.0ms
(* (/ 1 (* (cbrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (cbrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))) (/ (* 4.0 a) (/ (cbrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(* (/ 1 (* (cbrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (cbrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))) (/ (* 4.0 a) (/ (cbrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
173 → 173
Iterations

Useful iterations: 2 (372.0ms)

IterNodesCost
03057940
19377091
242354783
done50004783

prune517.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.3b

regimes253.0ms

Accuracy

81.6% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 31.9b

bsearch107.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
3.6627135292415903e+111
8
-4.854151311909829e-126
-9.294658666337375e-130
-4.7828589349284326e-126

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02839
13639
done3639

end0.0ms

sample1.2s

Algorithm
intervals
Results
263.0ms1110×body2560valid
230.0ms5789×body80valid
166.0ms885×body1280valid
111.0ms2998×body80nan
65.0ms448×body640valid
30.0ms253×body320valid
28.0ms101×body5120valid
9.0ms126×body160valid