Details

Time bar (total: 33.0s)

sample88.0ms

Algorithm
intervals
Results
24.0ms25×body2560valid
17.0ms182×body80valid
15.0ms33×body1280valid
7.0ms77×body80nan
6.0ms17×body640valid
3.0ms12×body320valid
3.0ms4×body5120valid
1.0ms5×body160valid

simplify144.0ms

Counts
1 → 1
Iterations
IterNodes
8134
7134
6132
5129
4126
3103
262
128
014

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.2b
(- (* b b) (* 4 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
22.6b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×times-frac add-cube-cbrt associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- insert-posit16 flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 81
Calls
4 calls:
80.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
14.0ms
(- (* b b) (* 4 (* a c)))
14.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
10.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
55.0ms
(- (* b b) (* 4 (* a c)))
103.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
114.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify2.1s

Counts
93 → 93
Iterations
IterNodes
34255
21194
1398
0154

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
1.2b
(- (* b b) (* 4 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
22.6b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
4×insert-posit16
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log cbrt-unprod pow-flip inv-pow
Counts
4 → 129
Calls
4 calls:
49.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
14.0ms
(- (* b b) (* 4 (* a c)))
20.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
15.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series444.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
67.0ms
(- (* b b) (* 4 (* a c)))
123.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
92.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify6.2s

Counts
141 → 141
Iterations
IterNodes
36319
21703
1554
0229

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize52.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
1.2b
(- (* b b) (* 4 (* a c)))
13.8b
(* (/ 1/2 a) (- 0 (* (* -4 c) a)))
22.6b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
15×*-un-lft-identity
13×associate-*l* add-cube-cbrt
10×times-frac
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×pow1
5×flip3-- flip--
4×sub-neg sqrt-prod insert-posit16
3×associate-*r*
2×distribute-rgt-in frac-times distribute-lft-in sqrt-div diff-log prod-exp associate-*r/ cbrt-unprod difference-of-squares unswap-sqr
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative distribute-rgt-neg-out div-inv distribute-lft-out-- sub0-neg
Counts
4 → 87
Calls
4 calls:
48.0ms
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
8.0ms
(- (* b b) (* 4 (* a c)))
31.0ms
(* (/ 1/2 a) (- 0 (* (* -4 c) a)))
8.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
68.0ms
(- (* b b) (* 4 (* a c)))
17.0ms
(* (/ 1/2 a) (- 0 (* (* -4 c) a)))
104.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify6.4s

Counts
99 → 99
Iterations
IterNodes
36165
21369
1470
0183

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2 c) (/ 1 (- (sqrt (- (* b b) (* 4 (* a c)))) b)))
1.1b
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
1.2b
(- (* b b) (* 4 (* a c)))
22.6b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
26×add-exp-log
24×associate-*r*
23×*-un-lft-identity
18×times-frac
16×add-cbrt-cube
15×add-cube-cbrt
12×prod-exp
10×pow1
8×add-log-exp difference-of-squares
7×sqrt-prod
6×cbrt-unprod
4×flip3-- div-exp insert-posit16 flip-- distribute-lft-out--
3×pow-prod-down
2×cbrt-undiv rec-exp sub-neg sqrt-div diff-log 1-exp associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 95
Calls
4 calls:
108.0ms
(* (* 2 c) (/ 1 (- (sqrt (- (* b b) (* 4 (* a c)))) b)))
37.0ms
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
8.0ms
(- (* b b) (* 4 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series530.0ms

Counts
4 → 12
Calls
4 calls:
280.0ms
(* (* 2 c) (/ 1 (- (sqrt (- (* b b) (* 4 (* a c)))) b)))
108.0ms
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
50.0ms
(- (* b b) (* 4 (* a c)))
92.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify5.5s

Counts
107 → 107
Iterations
IterNodes
35163
21547
1504
0184

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

regimes404.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.7b

bsearch645.0ms

Steps
ItersRangePoint
7
1.602087361235081e+82
9.448026055101687e+83
9.112814637305151e+83
8
-1.21170449760255e-224
-2.8092574063706908e-229
-2.9582179666484207e-229
8
-3.9150248283130293e+127
-1.4003686841431728e+125
-1.3422084503380959e+126

simplify8.0ms

Iterations
IterNodes
243
143
037

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.4s1036×body2560valid
860.0ms5858×body80valid
691.0ms953×body1280valid
417.0ms2920×body80nan
338.0ms466×body640valid
91.0ms103×body5120valid
82.0ms227×body320valid
28.0ms113×body160valid