Details

Time bar (total: 15.9s)

sample108.0ms

Algorithm
intervals
Results
64.0ms273×body80valid
17.0ms82×body80nan

simplify200.0ms

Counts
1 → 1
Iterations
IterNodes
done171
6171
5169
4155
3120
267
135
020

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize155.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite50.0ms

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-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 67
Calls
4 calls:
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
14.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
95.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
89.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
132.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify941.0ms

Counts
79 → 79
Iterations
IterNodes
done5001
21040
1259
0102

prune672.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize174.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
4.4b
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
6.0b
(/ a (/ b c))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
51×*-un-lft-identity
48×add-sqr-sqrt
47×add-cube-cbrt
21×add-cbrt-cube add-exp-log
14×associate-/r*
8×add-log-exp
7×cbrt-undiv div-exp
6×div-inv
5×pow1
4×prod-exp cbrt-unprod insert-posit16 associate-/l*
3×associate-/r/ sqrt-prod
2×clear-num sum-log frac-2neg flip3-- sqrt-div associate-*r/ flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log associate-+l- flip-+
Counts
4 → 127
Calls
4 calls:
17.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
26.0ms
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
6.0ms
(/ a (/ b c))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
69.0ms
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
35.0ms
(/ a (/ b c))
98.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.1s

Counts
139 → 139
Iterations
IterNodes
done5002
23935
1769
0281

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize203.0ms

Local error

Found 4 expressions with local error:

10.0b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 64
Calls
4 calls:
8.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
99.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
118.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
85.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify943.0ms

Counts
76 → 76
Iterations
IterNodes
done5000
21001
1239
091

prune663.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

localize173.0ms

Local error

Found 4 expressions with local error:

6.0b
(/ a (/ b c))
12.2b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
13×associate-/r*
9×add-cbrt-cube add-exp-log
8×add-log-exp
6×pow1 sqrt-prod
5×div-inv
4×sqrt-div insert-posit16
3×cbrt-undiv div-exp associate-/l*
2×rem-sqrt-square sum-log sqrt-pow1 flip3-- pow1/2 flip--
1×neg-sub0 +-commutative clear-num frac-2neg flip3-+ neg-log associate-/r/ associate-+l- flip-+
Counts
4 → 117
Calls
4 calls:
11.0ms
(/ a (/ b c))
17.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ a (/ b c))
126.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
85.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
108.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.4s

Counts
129 → 129
Iterations
IterNodes
done5002
22751
1605
0231

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.8b

regimes418.0ms

Accuracy

93.5% (0.9b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 19.3b

bsearch396.0ms

Steps
ItersRangePoint
10
1.0955696400612189e+91
1.0202913897586463e+104
8.119950078133889e+99
9
-2.409563002992963e+162
-2.0274263258127503e+155
-2.0519886074223697e+155

simplify19.0ms

Iterations
IterNodes
done51
151
043

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.5s8746×body80valid
617.0ms2913×body80nan