Details

Time bar (total: 43.6s)

sample127.0ms

Algorithm
intervals
Results
41.0ms148×body160valid
23.0ms256×body80nan
22.0ms512×pre80true
14.0ms48×body320valid
6.0ms60×body80valid

simplify161.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
161.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize30.0ms

Local error

Found 4 expressions with local error:

37.2b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(/ (/ (- (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)))

rewrite36.0ms

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
21.0ms
(/ (/ (- (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))

series386.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
101.0ms
(sqrt (fma c (* -4 a) (* b b)))
100.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
81.0ms
(fma c (* -4 a) (* b b))

simplify13.8s

Counts
225 → 191
Calls
225 calls:
Slowest
553.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) (sqrt 2)) (sqrt a))
397.0ms
(/ (/ (* (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)))
179.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
174.0ms
(/ (* (* (/ (- (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))
156.0ms
(/ (/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2)) (* (* a a) a))

prune2.4s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 39.9b

localize35.0ms

Local error

Found 4 expressions with local error:

42.8b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.2b
(/ (/ (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))

rewrite20.0ms

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 c (* -4 a) (* b b))
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))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
585.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
422.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
77.0ms
(fma c (* -4 a) (* b b))
65.0ms
(fma c (* -4 a) (* b b))

simplify9.7s

Counts
109 → 118
Calls
109 calls:
Slowest
558.0ms
(/ (/ (* (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)))
447.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
306.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
247.0ms
(/ (/ (* (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))) (sqrt a))
239.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))

prune1.8s

Pruning

40 alts after pruning (40 fresh and 0 done)

Merged error: 39.8b

localize51.0ms

Local error

Found 4 expressions with local error:

42.8b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.7b
(cbrt a)
0.7b
(cbrt a)
0.7b
(cbrt a)

rewrite3.0ms

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
1.0ms
(cbrt a)
1.0ms
(cbrt a)
1.0ms
(cbrt a)
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
447.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
308.0ms
(cbrt a)
275.0ms
(cbrt a)
255.0ms
(cbrt a)

simplify1.0s

Counts
21 → 65
Calls
21 calls:
Slowest
303.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
176.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
161.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
158.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
127.0ms
(* (pow (* a -1) 1/3) (cbrt -1))

prune1.2s

Pruning

45 alts after pruning (45 fresh and 0 done)

Merged error: 39.7b

localize78.0ms

Local error

Found 4 expressions with local error:

42.8b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.7b
(cbrt a)
0.7b
(cbrt a)
0.7b
(cbrt a)

rewrite3.0ms

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
1.0ms
(cbrt a)
1.0ms
(cbrt a)
1.0ms
(cbrt a)
1.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
396.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
310.0ms
(cbrt a)
262.0ms
(cbrt a)
257.0ms
(cbrt a)

simplify1.0s

Counts
21 → 65
Calls
21 calls:
Slowest
276.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
204.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
154.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
151.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
118.0ms
(* (pow (* a -1) 1/3) (cbrt -1))

prune1.1s

Pruning

47 alts after pruning (46 fresh and 1 done)

Merged error: 39.7b

regimes1.2s

Accuracy

0% (3.0b remaining)

Error of 43.4b against oracle of 40.4b and baseline of 43.4b

bsearch4.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
1.4s16371×pre80true
1.4s4872×body160valid
1.3s8371×body80nan
667.0ms1769×body80valid
540.0ms1359×body320valid