Details

Time bar (total: 16.3s)

sample52.0ms

Algorithm
intervals
Results
23.0ms286×body80valid
9.0ms103×body80nan

simplify159.0ms

Counts
1 → 1
Iterations
IterNodes
done152
7152
6151
5144
4132
3101
262
135
020

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize205.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite148.0ms

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:
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
54.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
119.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
85.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.0s

Counts
79 → 79
Iterations
IterNodes
done5000
32698
2773
1250
0102

prune732.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize218.0ms

Local error

Found 4 expressions with local error:

7.0b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite95.0ms

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:
24.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
27.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
113.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
109.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
136.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts
76 → 76
Iterations
IterNodes
done5002
32322
2669
1226
091

prune644.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.5b

localize211.0ms

Local error

Found 4 expressions with local error:

7.0b
(+ b (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×add-cbrt-cube add-exp-log insert-posit16
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
1×+-commutative sum-log flip3-+ flip-+
Counts
4 → 60
Calls
4 calls:
10.0ms
(+ b (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ b (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
97.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
93.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
84.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.0s

Counts
72 → 72
Iterations
IterNodes
done5011
32247
2645
1205
077

prune697.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.0b

localize195.0ms

Local error

Found 4 expressions with local error:

21.3b
(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)))

rewrite44.0ms

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:
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series559.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
154.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
134.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
142.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify2.1s

Counts
70 → 70
Iterations
IterNodes
done5002
31931
2578
1202
089

prune714.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.0b

regimes323.0ms

Accuracy

87% (1.6b remaining)

Error of 8.2b against oracle of 6.6b and baseline of 19.0b

bsearch306.0ms

Steps
ItersRangePoint
8
2.5230591910300896e+45
6.095379443414697e+48
5.966643100467746e+48
8
-5.8501169415505e+41
-1.816545290760657e+37
-5.748232111683622e+41

simplify16.0ms

Iterations
IterNodes
done68
368
265
155
044

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.1s8772×body80valid
393.0ms3077×body80nan