Details

Time bar (total: 21.8s)

sample64.0ms

Algorithm
intervals
Results
28.0ms285×body80valid
9.0ms106×body80nan

simplify166.0ms

Counts
1 → 1
Iterations
IterNodes
done158
7158
6157
5150
4138
3110
262
136
020

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize178.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-log-exp
9×add-cube-cbrt
6×pow1 sqrt-prod
4×expm1-log1p-u distribute-rgt-neg-in add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
3×distribute-lft-neg-in flip3-- flip--
2×rem-sqrt-square sum-log sqrt-pow1 pow1/2 distribute-lft-out
1×neg-sub0 +-commutative neg-mul-1 sub-neg flip3-+ fma-neg diff-log prod-diff neg-log associate-+l- flip-+
Counts
4 → 77
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (* b b) (* (* 4.0 a) c))
123.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.1s

Counts
89 → 89
Iterations
IterNodes
done5001
33363
2840
1268
0104

prune789.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize168.0ms

Local error

Found 4 expressions with local error:

8.0b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite75.0ms

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 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 → 88
Calls
4 calls:
14.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.7s

Counts
100 → 100
Iterations
IterNodes
done5000
32880
2822
1281
0115

prune948.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.1b

localize191.0ms

Local error

Found 4 expressions with local error:

10.9b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite74.0ms

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 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 → 76
Calls
4 calls:
20.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
126.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
88 → 88
Iterations
IterNodes
done5000
33221
2793
1247
090

prune946.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.1b

localize202.0ms

Local error

Found 4 expressions with local error:

24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
25.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
25.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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 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 → 62
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
152.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
119.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
119.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
74 → 74
Iterations
IterNodes
done5001
32150
2610
1216
094

prune850.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 8.1b

regimes479.0ms

Accuracy

93.9% (0.9b remaining)

Error of 6.6b against oracle of 5.7b and baseline of 20.1b

bsearch281.0ms

Steps
ItersRangePoint
8
1.0335802065380817e+152
4.346839969020365e+154
1.042426094136288e+152
8
-1.4137780731624028e+101
-4.084920897753177e+97
-1.3906582137854214e+101

simplify10.0ms

Iterations
IterNodes
done49
149
043

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.5s8718×body80valid
390.0ms2875×body80nan