Details

Time bar (total: 24.8s)

sample121.0ms

Algorithm
intervals
Results
78.0ms272×body80valid
19.0ms99×body80nan

simplify175.0ms

Counts
1 → 1
Iterations
IterNodes
8152
7152
6151
5144
4132
3101
262
135
020

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize189.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4 a) c))
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
24.5b
(sqrt (- (* b b) (* (* 4 a) c)))
24.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip--
3×diff-log
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 64
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4 a) c))
28.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 4 a) c))
104.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
128.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.3s

Counts
76 → 76
Iterations
IterNodes
32593
2742
1237
099

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize157.0ms

Local error

Found 4 expressions with local error:

9.5b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
24.5b
(sqrt (- (* b b) (* (* 4 a) c)))
24.5b
(sqrt (- (* b b) (* (* 4 a) c)))
24.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×add-cbrt-cube add-exp-log insert-posit16
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
2×sum-log
1×neg-sub0 +-commutative flip3-+ neg-log associate-+l- flip-+
Counts
4 → 62
Calls
4 calls:
17.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
95.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
116.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
126.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.0s

Counts
74 → 74
Iterations
IterNodes
32327
2716
1230
087

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize183.0ms

Local error

Found 4 expressions with local error:

24.5b
(sqrt (- (* b b) (* (* 4 a) c)))
25.3b
(cbrt (- (* b b) (* (* 4 a) c)))
25.3b
(cbrt (- (* b b) (* (* 4 a) c)))
25.3b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series508.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
149.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
110.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
147.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify4.2s

Counts
70 → 70
Iterations
IterNodes
46322
31876
2580
1200
089

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.5b

localize192.0ms

Local error

Found 4 expressions with local error:

24.5b
(sqrt (- (* b b) (* (* 4 a) c)))
24.5b
(sqrt (- (* b b) (* (* 4 a) c)))
25.3b
(cbrt (- (* b b) (* (* 4 a) c)))
25.3b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×cbrt-div flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 60
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
17.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
122.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
131.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
133.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify4.7s

Counts
72 → 72
Iterations
IterNodes
46322
31876
2580
1200
089

prune1.6s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.5b

regimes560.0ms

Accuracy

89.5% (1.3b remaining)

Error of 8.0b against oracle of 6.7b and baseline of 19.3b

bsearch367.0ms

Steps
ItersRangePoint
9
1.9710174875302874e+32
1.945305249879839e+37
1.37593608973837e+37
8
-3.585760457965514e+97
-4.884785332531034e+94
-1.56549847594674e+97

simplify21.0ms

Iterations
IterNodes
253
153
043

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.5s8694×body80valid
729.0ms2862×body80nan