Details

Time bar (total: 19.3s)

sample126.0ms

Algorithm
intervals
Results
44.0ms34×body2560valid
24.0ms198×body80valid
17.0ms29×body1280valid
11.0ms91×body80nan
3.0ms8×body640valid
2.0ms7×body320valid
2.0ms2×body5120valid
1.0ms6×body160valid

simplify110.0ms

Counts
1 → 1
Iterations
IterNodes
895
795
694
592
484
367
243
124
014

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4 a) c)
1.2b
(- (* b b) (* (* 4 a) c))
1.3b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
27.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
16.0ms
(* (* 4 a) c)
15.0ms
(- (* b b) (* (* 4 a) c))
64.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (* 4 a) c)
55.0ms
(- (* b b) (* (* 4 a) c))
137.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
105.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.1s

Counts
76 → 76
Iterations
IterNodes
33519
2957
1298
0123

prune851.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* -4 a) c)
1.2b
(+ (* (* -4 a) c) (* b b))
1.3b
(- (sqrt (+ (* (* -4 a) c) (* b b))) b)
27.8b
(sqrt (+ (* (* -4 a) c) (* b b)))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×flip3-+ sqrt-div flip-+ difference-of-squares
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 flip3-- pow1/2 diff-log associate-*l* *-commutative flip-- distribute-lft-out--
Counts
4 → 63
Calls
4 calls:
29.0ms
(* (* -4 a) c)
30.0ms
(+ (* (* -4 a) c) (* b b))
151.0ms
(- (sqrt (+ (* (* -4 a) c) (* b b))) b)
33.0ms
(sqrt (+ (* (* -4 a) c) (* b b)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (* -4 a) c)
82.0ms
(+ (* (* -4 a) c) (* b b))
105.0ms
(- (sqrt (+ (* (* -4 a) c) (* b b))) b)
145.0ms
(sqrt (+ (* (* -4 a) c) (* b b)))

simplify2.1s

Counts
75 → 75
Iterations
IterNodes
33617
2945
1273
0113

prune681.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt c)
1.2b
(+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))
1.3b
(- (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))) b)
27.8b
(sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log sqrt-prod insert-posit16
3×cbrt-prod
2×flip3-+ sqrt-div flip-+ difference-of-squares
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 flip3-- pow1/2 pow1/3 diff-log flip-- distribute-lft-out--
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt c)
78.0ms
(+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))
767.0ms
(- (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))) b)
194.0ms
(sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))

series642.0ms

Counts
4 → 12
Calls
4 calls:
253.0ms
(cbrt c)
95.0ms
(+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))
152.0ms
(- (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))) b)
141.0ms
(sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))

simplify1.4s

Counts
68 → 68
Iterations
IterNodes
33680
2791
1240
0106

prune768.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.0b

localize71.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))
13.1b
(- (* (sqrt (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))) (sqrt (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))))) b)
27.8b
(sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))
27.8b
(sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))

rewrite833.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log sub-neg flip3-- diff-log flip-- difference-of-squares
Counts
4 → 58
Calls
4 calls:
108.0ms
(+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))
340.0ms
(- (* (sqrt (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))) (sqrt (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))))) b)
200.0ms
(sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))
184.0ms
(sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))

series474.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))
143.0ms
(- (* (sqrt (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))) (sqrt (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))))) b)
112.0ms
(sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))
115.0ms
(sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))

simplify787.0ms

Counts
70 → 70
Iterations
IterNodes
32636
2618
1203
088

prune919.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.0b

regimes318.0ms

Accuracy

86.7% (3.0b remaining)

Error of 14.0b against oracle of 11.0b and baseline of 33.5b

bsearch245.0ms

Steps
ItersRangePoint
8
2.764110880089542e-64
2.3245141193625934e-60
2.2927953806734678e-60
8
-3.527365539031458e+131
-2.6175232982162155e+128
-1.178432289663324e+129

simplify11.0ms

Iterations
IterNodes
237
137
031

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.1s908×body1280valid
908.0ms1054×body2560valid
905.0ms5886×body80valid
694.0ms446×body640valid
382.0ms2993×body80nan
157.0ms110×body5120valid
114.0ms232×body320valid
57.0ms113×body160valid