Details

Time bar (total: 22.4s)

sample57.0ms

Algorithm
intervals
Results
27.0ms284×body80valid
11.0ms85×body80nan

simplify182.0ms

Counts
1 → 1
Iterations
IterNodes
done160
7160
6159
5152
4140
3108
263
136
020

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize175.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log 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 → 155
Calls
4 calls:
37.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
45.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
24.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
29.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
93.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
101.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
104.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.1s

Counts
167 → 167
Iterations
IterNodes
done5000
34570
21211
1436
0181

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.7b

localize184.0ms

Local error

Found 4 expressions with local error:

11.8b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×fma-def *-un-lft-identity add-cube-cbrt
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-- pow1/2 flip--
2×sum-log
1×neg-sub0 +-commutative neg-mul-1 flip3-+ neg-log associate-+l- flip-+
Counts
4 → 80
Calls
4 calls:
28.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
105.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
105.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
103.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.9s

Counts
92 → 92
Iterations
IterNodes
done5001
33147
2801
1250
091

prune910.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize144.0ms

Local error

Found 4 expressions with local error:

9.3b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 92
Calls
4 calls:
16.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
92.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
86.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
96.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.5s

Counts
104 → 104
Iterations
IterNodes
done5001
32769
2826
1284
0116

prune982.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize184.0ms

Local error

Found 4 expressions with local error:

21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
22.0b
(cbrt (- (* b b) (* (* 4 a) c)))
22.0b
(cbrt (- (* b b) (* (* 4 a) c)))
22.0b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 66
Calls
4 calls:
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
18.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series530.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
165.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
142.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
140.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify2.0s

Counts
78 → 78
Iterations
IterNodes
done5002
32070
2609
1215
093

prune835.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

regimes389.0ms

Accuracy

84.5% (2.2b remaining)

Error of 7.6b against oracle of 5.4b and baseline of 19.6b

bsearch280.0ms

Steps
ItersRangePoint
8
4.664337482673326e-05
0.17679972651571432
0.17389787404847717
7
-2.6305624027095992e+48
-2.971125736392027e+46
-2.593460638040052e+48

simplify11.0ms

Iterations
IterNodes
done54
154
044

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.0s8783×body80valid
660.0ms2988×body80nan