Details

Time bar (total: 51.7s)

sample333.0ms

Algorithm
intervals
Results
54.0ms240×body80nan
35.0ms115×body320valid
24.0ms496×pre80true
18.0ms90×body160valid
8.0ms17×body640valid
4.0ms34×body80valid

simplify226.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
225.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize53.0ms

Local error

Found 4 expressions with local error:

24.7b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.1b
(fma c (* -4 a) (* b b))
0.0b
(sqrt (fma c (* -4 a) (* b b)))

rewrite90.0ms

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
19.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
16.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
5.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series580.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
264.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
140.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
105.0ms
(sqrt (fma c (* -4 a) (* b b)))
71.0ms
(fma c (* -4 a) (* b b))

simplify14.8s

Counts
225 → 191
Calls
225 calls:
Slowest
801.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
232.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
197.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
180.0ms
(/ (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* a a) a))
165.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) 1)

prune2.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 49.2b

localize56.0ms

Local error

Found 4 expressions with local error:

51.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.1b
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
0.1b
(fma c (* -4 a) (* b b))
0.1b
(fma c (* -4 a) (* b b))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
46×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×associate-/l*
9×add-cbrt-cube add-exp-log
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* div-exp fma-udef
1×clear-num frac-2neg associate-/l/
Counts
4 → 106
Calls
4 calls:
Slowest
15.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
1.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma c (* -4 a) (* b b))
0.0ms
(fma c (* -4 a) (* b b))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
626.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
439.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
67.0ms
(fma c (* -4 a) (* b b))
65.0ms
(fma c (* -4 a) (* b b))

simplify10.1s

Counts
109 → 118
Calls
109 calls:
Slowest
513.0ms
(/ (/ (* (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
413.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
310.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
265.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
251.0ms
(/ (/ (* (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))) (sqrt 2)) (* (cbrt a) (cbrt a)))

prune1.5s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 49.1b

localize57.0ms

Local error

Found 4 expressions with local error:

51.9b
(fma (sqrt (sqrt (* (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))) (cbrt (fma c (* -4 a) (* b b)))))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.5b
(cbrt (fma c (* -4 a) (* b b)))
0.5b
(cbrt (fma c (* -4 a) (* b b)))
0.5b
(cbrt (fma c (* -4 a) (* b b)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 53
Calls
4 calls:
Slowest
2.0ms
(cbrt (fma c (* -4 a) (* b b)))
1.0ms
(cbrt (fma c (* -4 a) (* b b)))
1.0ms
(cbrt (fma c (* -4 a) (* b b)))
1.0ms
(fma (sqrt (sqrt (* (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))) (cbrt (fma c (* -4 a) (* b b)))))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
402.0ms
(fma (sqrt (sqrt (* (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))) (cbrt (fma c (* -4 a) (* b b)))))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
271.0ms
(cbrt (fma c (* -4 a) (* b b)))
262.0ms
(cbrt (fma c (* -4 a) (* b b)))
230.0ms
(cbrt (fma c (* -4 a) (* b b)))

simplify3.3s

Counts
21 → 65
Calls
21 calls:
Slowest
379.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
365.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
352.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
317.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
308.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.4s

Pruning

40 alts after pruning (40 fresh and 0 done)

Merged error: 49.0b

localize92.0ms

Local error

Found 4 expressions with local error:

51.4b
(fma (sqrt (sqrt (* (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))) (pow (fma c (* -4 a) (* b b)) 1/3)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
2.9b
(pow (fma c (* -4 a) (* b b)) 1/3)
0.5b
(cbrt (fma c (* -4 a) (* b b)))
0.5b
(cbrt (fma c (* -4 a) (* b b)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-prod
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow unpow-prod-down
2×pow1/3
1×pow-to-exp pow-pow unpow1/3 pow-exp fma-udef sqr-pow
Counts
4 → 60
Calls
4 calls:
Slowest
14.0ms
(pow (fma c (* -4 a) (* b b)) 1/3)
1.0ms
(cbrt (fma c (* -4 a) (* b b)))
1.0ms
(cbrt (fma c (* -4 a) (* b b)))
1.0ms
(fma (sqrt (sqrt (* (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))) (pow (fma c (* -4 a) (* b b)) 1/3)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
438.0ms
(fma (sqrt (sqrt (* (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))) (pow (fma c (* -4 a) (* b b)) 1/3)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
293.0ms
(cbrt (fma c (* -4 a) (* b b)))
276.0ms
(pow (fma c (* -4 a) (* b b)) 1/3)
255.0ms
(cbrt (fma c (* -4 a) (* b b)))

simplify4.3s

Counts
25 → 72
Calls
25 calls:
Slowest
662.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))
405.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
398.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
391.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
362.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune1.2s

Pruning

46 alts after pruning (46 fresh and 0 done)

Merged error: 49.0b

regimes1.2s

Accuracy

0% (1.7b remaining)

Error of 50.7b against oracle of 49.0b and baseline of 50.7b

bsearch8.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
1.6s3561×body320valid
1.3s3021×body160valid
1.2s16290×pre80true
1.2s8290×body80nan
331.0ms527×body640valid
139.0ms891×body80valid