Details

Time bar (total: 30.6s)

sample130.0ms

Algorithm
intervals
Results
82.0ms276×body80valid
20.0ms96×body80nan

simplify123.0ms

Counts
1 → 1
Iterations
IterNodes
8160
7160
6159
5152
4140
3108
263
136
020

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.5b

localize163.0ms

Local error

Found 4 expressions with local error:

1.2b
(fma -4 (* c a) (* b b))
1.4b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
20.1b
(sqrt (fma -4 (* c a) (* b b)))
20.1b
(sqrt (fma -4 (* c a) (* b b)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- neg-log fma-udef flip--
Counts
4 → 130
Calls
4 calls:
0.0ms
(fma -4 (* c a) (* b b))
18.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
4.0ms
(sqrt (fma -4 (* c a) (* b b)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(fma -4 (* c a) (* b b))
94.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
112.0ms
(sqrt (fma -4 (* c a) (* b b)))
138.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify4.7s

Counts
142 → 142
Iterations
IterNodes
45888
31831
2709
1328
0154

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.2b

localize161.0ms

Local error

Found 4 expressions with local error:

1.2b
(fma -4 (* c a) (* b b))
1.4b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
20.1b
(sqrt (fma (* -4 c) a (* b b)))
20.1b
(sqrt (fma -4 (* c a) (* b b)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- neg-log fma-udef flip--
Counts
4 → 130
Calls
4 calls:
0.0ms
(fma -4 (* c a) (* b b))
9.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.0ms
(sqrt (fma (* -4 c) a (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(fma -4 (* c a) (* b b))
119.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
119.0ms
(sqrt (fma (* -4 c) a (* b b)))
100.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify5.4s

Counts
142 → 142
Iterations
IterNodes
47678
31982
2732
1344
0170

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize149.0ms

Local error

Found 4 expressions with local error:

8.3b
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
20.1b
(sqrt (fma -4 (* c a) (* b b)))
20.1b
(sqrt (fma -4 (* c a) (* b b)))
20.1b
(sqrt (fma (* -4 c) a (* b b)))

rewrite12.0ms

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
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip-- difference-of-squares
Counts
4 → 82
Calls
4 calls:
8.0ms
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma (* -4 c) a (* b b)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
129.0ms
(sqrt (fma -4 (* c a) (* b b)))
103.0ms
(sqrt (fma -4 (* c a) (* b b)))
104.0ms
(sqrt (fma (* -4 c) a (* b b)))

simplify2.5s

Counts
94 → 94
Iterations
IterNodes
44027
31433
2512
1225
0111

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.1b

localize193.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (fma (* -4 c) a (* b b))) b)
1.4b
(+ (sqrt (fma (* -4 c) a (* b b))) b)
20.1b
(sqrt (fma (* -4 c) a (* b b)))
20.1b
(sqrt (fma (* -4 c) a (* b b)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×*-un-lft-identity
22×add-cube-cbrt sqrt-prod
18×prod-diff
8×add-log-exp
6×pow1 fma-def fma-neg
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2 difference-of-squares
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out distribute-lft-out--
Counts
4 → 91
Calls
4 calls:
12.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
6.0ms
(+ (sqrt (fma (* -4 c) a (* b b))) b)
1.0ms
(sqrt (fma (* -4 c) a (* b b)))
1.0ms
(sqrt (fma (* -4 c) a (* b b)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
118.0ms
(+ (sqrt (fma (* -4 c) a (* b b))) b)
130.0ms
(sqrt (fma (* -4 c) a (* b b)))
102.0ms
(sqrt (fma (* -4 c) a (* b b)))

simplify3.3s

Counts
103 → 103
Iterations
IterNodes
44249
31554
2456
1192
098

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

regimes367.0ms

Accuracy

91.3% (0.6b remaining)

Error of 12.7b against oracle of 12.1b and baseline of 19.1b

bsearch179.0ms

Steps
ItersRangePoint
9
1.5347927881719531e+137
5.414027326126016e+143
1.673041355293174e+137

simplify15.0ms

Iterations
IterNodes
338
238
137
032

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.7s8792×body80valid
980.0ms2909×body80nan