Details

Time bar (total: 26.0s)

sample83.0ms

Algorithm
intervals
Results
17.0ms141×body160valid
14.0ms239×body80nan
13.0ms495×pre80true
10.0ms50×body320valid
4.0ms65×body80valid

simplify134.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
36.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(- (* b b) (* (* 4.0 a) c))
93.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series473.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms
(- (* b b) (* (* 4.0 a) c))
181.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
108.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01671697
14331584
214811361
done50001347

prune406.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
119.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
93.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series692.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(- (* b b) (* (* 4.0 a) c))
241.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
260.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.3s

Counts
243 → 243
Iterations

Useful iterations: done (2.2s)

IterNodesCost
034010026
18127598
232366483
done50016397

prune938.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (* 4.0 (* a c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(* (/ (sqrt (* 4.0 (* a c))) 2.0) (/ (sqrt (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
0.3b
(/ (sqrt (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite300.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
21×add-sqr-sqrt times-frac
16×add-cube-cbrt *-un-lft-identity associate-*l*
12×pow1
10×associate-*r*
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×sqrt-prod
6×add-log-exp
5×associate-*r/
4×expm1-log1p-u pow-prod-down associate-/r/ log1p-expm1-u associate-/l*
3×flip3-- sqrt-pow1 flip-- div-inv
2×unswap-sqr
1×frac-times sub-neg frac-2neg pow1/2 fma-neg diff-log prod-diff associate-*l/ clear-num associate-/r* *-commutative
Counts
4 → 111
Calls
4 calls:
14.0ms
(sqrt (* 4.0 (* a c)))
17.0ms
(- (* b b) (* (* 4.0 a) c))
187.0ms
(* (/ (sqrt (* 4.0 (* a c))) 2.0) (/ (sqrt (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
78.0ms
(/ (sqrt (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
152.0ms
(sqrt (* 4.0 (* a c)))
89.0ms
(- (* b b) (* (* 4.0 a) c))
613.0ms
(* (/ (sqrt (* 4.0 (* a c))) 2.0) (/ (sqrt (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
620.0ms
(/ (sqrt (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify2.3s

Counts
123 → 123
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02373451
16733012
229612489
done50012483

prune638.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 0 (* (* a c) 4.0)) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))
0.4b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))) (/ (* 2.0 a) (fma b b (- (- (* b b) (* 4.0 (* a c))) (* b (sqrt (- (* b b) (* (* 4.0 a) c))))))))
0.4b
(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
35.8b
(- (- (* b b) (* 4.0 (* a c))) (* b (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite890.0ms

Algorithm
rewrite-expression-head
Rules
2172×times-frac
1681×add-sqr-sqrt
1121×*-un-lft-identity
672×difference-of-squares
622×unpow-prod-down cube-prod
617×add-cube-cbrt
281×sqr-pow
252×distribute-lft-out--
230×sqrt-prod
128×div-inv
120×associate-/l*
112×distribute-rgt-neg-in
44×associate-/r*
28×difference-cubes add-exp-log add-cbrt-cube
19×associate-/r/
15×flip3-- flip--
14×cbrt-undiv div-exp
9×add-log-exp
6×pow1 sqrt-div
4×expm1-log1p-u associate-*r/ prod-diff frac-sub log1p-expm1-u
3×pow-unpow pow-pow fma-neg diff-log associate--l+ associate-/l/
2×cube-div sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- cube-mult pow-to-exp sqrt-pow1 flip3-+ pow1/2 unpow3 pow-exp sqrt-pow2 flip-+ rem-cube-cbrt
Counts
4 → 1203
Calls
4 calls:
228.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))
386.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))) (/ (* 2.0 a) (fma b b (- (- (* b b) (* 4.0 (* a c))) (* b (sqrt (- (* b b) (* (* 4.0 a) c))))))))
26.0ms
(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
98.0ms
(- (- (* b b) (* 4.0 (* a c))) (* b (sqrt (- (* b b) (* (* 4.0 a) c)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
513.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))
606.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))) (/ (* 2.0 a) (fma b b (- (- (* b b) (* 4.0 (* a c))) (* b (sqrt (- (* b b) (* (* 4.0 a) c))))))))
63.0ms
(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
203.0ms
(- (- (* b b) (* 4.0 (* a c))) (* b (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.5s

Counts
1215 → 1215
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01100108144
1319898803
done500097694

prune5.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes168.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01925
12523
done2523

end0.0ms

sample4.2s

Algorithm
intervals
Results
888.0ms1350×body320valid
826.0ms16396×pre80true
761.0ms4869×body160valid
672.0ms8396×body80nan
257.0ms1781×body80valid