Details

Time bar (total: 21.7s)

sample57.0ms

Algorithm
intervals
Results
25.0ms286×body80valid
10.0ms103×body80nan

simplify247.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize177.0ms

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)))

rewrite141.0ms

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:
38.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
33.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
134.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
97.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
111.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.6s

Counts
167 → 167
Iterations
IterNodes
done5000
34570
21211
1436
0181

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.5b

localize206.0ms

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)))

rewrite49.0ms

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:
16.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series494.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
130.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
141.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
126.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify1.8s

Counts
78 → 78
Iterations
IterNodes
done5002
32070
2609
1215
093

prune901.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize152.0ms

Local error

Found 4 expressions with local error:

5.4b
(exp (log (sqrt (- (* b b) (* (* 4 a) c)))))
12.6b
(- (- b) (exp (log (sqrt (- (* b b) (* (* 4 a) c))))))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
90×prod-diff
77×add-sqr-sqrt
73×*-un-lft-identity
69×add-cube-cbrt
68×log-prod exp-sum
40×sqrt-prod
31×distribute-rgt-neg-in
30×distribute-lft-neg-in
10×neg-mul-1 fma-neg
8×pow1 add-log-exp
6×exp-prod sqrt-div
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×sqrt-pow1 pow1/2 log-pow difference-of-squares
2×rem-sqrt-square log-div exp-diff diff-log distribute-lft-out--
1×associate--l- neg-sub0 sub-neg neg-log rem-exp-log
Counts
4 → 183
Calls
4 calls:
14.0ms
(exp (log (sqrt (- (* b b) (* (* 4 a) c)))))
56.0ms
(- (- b) (exp (log (sqrt (- (* b b) (* (* 4 a) c))))))
24.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(exp (log (sqrt (- (* b b) (* (* 4 a) c)))))
140.0ms
(- (- b) (exp (log (sqrt (- (* b b) (* (* 4 a) c))))))
86.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
113.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.7s

Counts
195 → 195
Iterations
IterNodes
done5000
34086
21244
1540
0247

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize220.0ms

Local error

Found 4 expressions with local error:

4.3b
(- (- b) (* (fabs (cbrt (fma -4 (* a c) (* b b)))) (sqrt (cbrt (fma -4 (* a c) (* b b))))))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))
22.0b
(cbrt (fma -4 (* a c) (* b b)))
22.0b
(cbrt (fma -4 (* a c) (* b b)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×fma-neg prod-diff
8×add-log-exp
6×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×sqrt-prod
2×neg-mul-1 flip3-- pow1/3 sqrt-div diff-log flip--
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 pow1/2 neg-log
Counts
4 → 83
Calls
4 calls:
21.0ms
(- (- b) (* (fabs (cbrt (fma -4 (* a c) (* b b)))) (sqrt (cbrt (fma -4 (* a c) (* b b))))))
13.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
1.0ms
(cbrt (fma -4 (* a c) (* b b)))
1.0ms
(cbrt (fma -4 (* a c) (* b b)))

series776.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (- b) (* (fabs (cbrt (fma -4 (* a c) (* b b)))) (sqrt (cbrt (fma -4 (* a c) (* b b))))))
129.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
271.0ms
(cbrt (fma -4 (* a c) (* b b)))
256.0ms
(cbrt (fma -4 (* a c) (* b b)))

simplify1.6s

Counts
95 → 95
Iterations
IterNodes
done5002
21402
1456
0187

prune991.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.0b

regimes400.0ms

Accuracy

86.6% (1.7b remaining)

Error of 8.3b against oracle of 6.6b and baseline of 19.1b

bsearch286.0ms

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

simplify42.0ms

Iterations
IterNodes
done67
167
057

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.6s8772×body80valid
331.0ms3077×body80nan