Details

Time bar (total: 1.4m)

sample436.0ms

Algorithm
intervals
Results
132.0ms41×body2560valid
98.0ms188×body80valid
19.0ms25×body1280valid
17.0ms91×body80nan
7.0ms11×body640valid
5.0ms10×body320valid
1.0ms5×body160valid

simplify187.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
186.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize41.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (- (* b_2 b_2) (* a c)))
1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 122
Calls
4 calls:
Slowest
88.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
67.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
33.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
109.0ms
(sqrt (- (* b_2 b_2) (* a c)))
103.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
49.0ms
(- (* b_2 b_2) (* a c))

simplify10.9s

Counts
182 → 134
Calls
182 calls:
Slowest
475.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
383.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
358.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
355.0ms
(* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
352.0ms
(- (pow (* b_2 b_2) 3) (pow (* a c) 3))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize33.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (- (* b_2 b_2) (* a c)))
1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (* b_2 b_2) (* a c))
0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
19×prod-diff
17×sqrt-prod
13×associate-*r* add-exp-log
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u difference-of-squares
3×unswap-sqr
2×frac-times sub-neg sqrt-div diff-log div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 123
Calls
4 calls:
Slowest
97.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
59.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series383.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
101.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))
48.0ms
(- (* b_2 b_2) (* a c))

simplify15.4s

Counts
166 → 135
Calls
166 calls:
Slowest
604.0ms
(sqrt (+ (* (* b_2 b_2) (* b_2 b_2)) (+ (* (* a c) (* a c)) (* (* b_2 b_2) (* a c)))))
578.0ms
(* (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
466.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
425.0ms
(exp (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a)))
392.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize28.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (- (* b_2 b_2) (* a c)))
1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (* b_2 b_2) (* a c))
0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- fma-neg div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-flip inv-pow
Counts
4 → 200
Calls
4 calls:
Slowest
80.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
47.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
118.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))
50.0ms
(- (* b_2 b_2) (* a c))

simplify31.5s

Counts
312 → 212
Calls
312 calls:
Slowest
553.0ms
(/ (* (* 1 1) 1) (/ (* (* a a) a) (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
526.0ms
(* (* (/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
480.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
440.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
439.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))))

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize19.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (- (* b_2 b_2) (* a c)))
1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 122
Calls
4 calls:
Slowest
65.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
59.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
100.0ms
(sqrt (- (* b_2 b_2) (* a c)))
92.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
49.0ms
(- (* b_2 b_2) (* a c))

simplify10.5s

Counts
182 → 134
Calls
182 calls:
Slowest
506.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
363.0ms
(+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (+ (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2)))
362.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
335.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
309.0ms
(+ (* (* b_2 b_2) (* b_2 b_2)) (+ (* (* a c) (* a c)) (* (* b_2 b_2) (* a c))))

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.2b

regimes428.0ms

Accuracy

87.6% (3.4b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 33.1b

bsearch333.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.4s1062×body2560valid
815.0ms5872×body80valid
450.0ms877×body1280valid
404.0ms2829×body80nan
181.0ms443×body640valid
92.0ms238×body320valid
75.0ms103×body5120valid
20.0ms111×body160valid