Details

Time bar (total: 33.4s)

sample171.0ms

Algorithm
intervals
Results
57.0ms150×body160valid
37.0ms267×body80nan
34.0ms523×pre80true
16.0ms106×body80valid

simplify186.0ms

Counts
1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize32.0ms

Local error

Found 4 expressions with local error:

29.3b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.3b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.2b
(fma c (* -4 a) (* b b))
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
Slowest
26.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
8.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series411.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
106.0ms
(sqrt (fma c (* -4 a) (* b b)))
100.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
86.0ms
(fma c (* -4 a) (* b b))

simplify836.0ms

Counts
191 → 191

prune2.3s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 26.4b

localize48.0ms

Local error

Found 4 expressions with local error:

28.1b
(- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b)))
0.3b
(/ (- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
0.3b
(* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))))
0.3b
(/ (/ (/ (- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b)))) 2) a)

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
504×times-frac
279×add-sqr-sqrt
233×*-un-lft-identity add-cube-cbrt
56×associate-/l*
42×pow3
41×difference-cubes cube-unmult
18×div-inv
17×add-cbrt-cube add-exp-log
9×pow1
7×cbrt-undiv div-exp
6×associate-/r* associate-*r* add-log-exp
4×expm1-log1p-u div-sub sqrt-prod insert-posit16 log1p-expm1-u
3×associate-*l* associate-/l/
2×clear-num frac-2neg flip3-- pow-prod-up flip-- unswap-sqr
1×sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 315
Calls
4 calls:
Slowest
68.0ms
(/ (/ (/ (- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b)))) 2) a)
35.0ms
(/ (- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
33.0ms
(- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b)))
7.0ms
(* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))))

series3.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))))
1.3s
(- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b)))
542.0ms
(/ (/ (/ (- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b)))) 2) a)
495.0ms
(/ (- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))

simplify1.4s

Counts
327 → 327

prune4.6s

Pruning

45 alts after pruning (45 fresh and 0 done)

Merged error: 25.2b

localize75.0ms

Local error

Found 4 expressions with local error:

62.0b
(fma (- (* b b)) b (* (* b b) b))
28.1b
(- (* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b))) (* (* b b) b))
0.3b
(/ (+ (- (* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b))) (* (* b b) b)) (fma (- (* b b)) b (* (* b b) b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
0.3b
(* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b)))

rewrite290.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
22×add-sqr-sqrt
16×add-cube-cbrt
12×times-frac
10×pow1
8×add-cbrt-cube add-exp-log
6×associate-*l* add-log-exp
5×fma-udef
4×expm1-log1p-u sqrt-prod insert-posit16 log1p-expm1-u distribute-lft-out associate-/l*
3×associate-/r* associate-*r*
2×distribute-rgt-in distribute-lft-in sqrt-pow1 pow-plus pow1/2 cube-unmult associate--l+ pow-prod-up unswap-sqr associate-/l/
1×difference-cubes cbrt-undiv clear-num sub-neg frac-2neg flip3-+ flip3-- fma-neg diff-log div-sub div-exp prod-diff pow3 pow-prod-down prod-exp *-commutative associate-+l- cbrt-unprod flip-+ div-inv flip--
Counts
4 → 100
Calls
4 calls:
Slowest
263.0ms
(/ (+ (- (* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b))) (* (* b b) b)) (fma (- (* b b)) b (* (* b b) b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
16.0ms
(- (* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b))) (* (* b b) b))
9.0ms
(* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b)))
0.0ms
(fma (- (* b b)) b (* (* b b) b))

series3.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b)))
1.3s
(- (* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b))) (* (* b b) b))
622.0ms
(/ (+ (- (* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b))) (* (* b b) b)) (fma (- (* b b)) b (* (* b b) b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
127.0ms
(fma (- (* b b)) b (* (* b b) b))

simplify2.0s

Counts
112 → 112

prune2.1s

Pruning

53 alts after pruning (53 fresh and 0 done)

Merged error: 24.7b

localize61.0ms

Local error

Found 4 expressions with local error:

62.0b
(fma (- (* b b)) b (* (* b b) b))
29.6b
(- (* (* b b) (sqrt (fma (* a -4) c (* b b)))) (* (* b b) b))
0.4b
(/ (+ (+ (* (* (* a -4) c) (sqrt (fma (* a -4) c (* b b)))) (- (* (* b b) (sqrt (fma (* a -4) c (* b b)))) (* (* b b) b))) (fma (- (* b b)) b (* (* b b) b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
0.3b
(* (* (* a -4) c) (sqrt (fma (* a -4) c (* b b))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
15×add-sqr-sqrt add-cbrt-cube add-exp-log add-cube-cbrt
13×pow1
12×times-frac
6×associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out associate-/l*
3×associate-/r* sqrt-prod
2×associate-/l/
1×cbrt-undiv clear-num associate-+r- sub-neg frac-2neg flip3-+ flip3-- fma-neg diff-log div-sub div-exp associate-*l* prod-diff *-commutative associate-+l- flip-+ fma-udef div-inv flip-- distribute-lft-out--
Counts
4 → 93
Calls
4 calls:
Slowest
1.3s
(/ (+ (+ (* (* (* a -4) c) (sqrt (fma (* a -4) c (* b b)))) (- (* (* b b) (sqrt (fma (* a -4) c (* b b)))) (* (* b b) b))) (fma (- (* b b)) b (* (* b b) b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
78.0ms
(* (* (* a -4) c) (sqrt (fma (* a -4) c (* b b))))
27.0ms
(- (* (* b b) (sqrt (fma (* a -4) c (* b b)))) (* (* b b) b))
0.0ms
(fma (- (* b b)) b (* (* b b) b))

series942.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
522.0ms
(/ (+ (+ (* (* (* a -4) c) (sqrt (fma (* a -4) c (* b b)))) (- (* (* b b) (sqrt (fma (* a -4) c (* b b)))) (* (* b b) b))) (fma (- (* b b)) b (* (* b b) b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
156.0ms
(- (* (* b b) (sqrt (fma (* a -4) c (* b b)))) (* (* b b) b))
138.0ms
(* (* (* a -4) c) (sqrt (fma (* a -4) c (* b b))))
126.0ms
(fma (- (* b b)) b (* (* b b) b))

simplify863.0ms

Counts
105 → 105

prune1.6s

Pruning

54 alts after pruning (54 fresh and 0 done)

Merged error: 23.7b

regimes1.6s

Accuracy

0% (2.5b remaining)

Error of 25.4b against oracle of 22.9b and baseline of 25.4b

bsearch9.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.5s4413×body160valid
1.5s8642×body80nan
939.0ms16642×pre80true
534.0ms3587×body80valid