Details

Time bar (total: 40.4s)

sample188.0ms

Algorithm
intervals
Results
54.0ms166×body160valid
46.0ms218×body80nan
33.0ms474×pre80true
22.0ms45×body320valid
7.0ms45×body80valid

simplify153.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
153.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.5b

localize21.0ms

Local error

Found 4 expressions with local error:

41.4b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(fma c (* -4 a) (* b b))
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite27.0ms

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
15.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
8.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series431.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(sqrt (fma c (* -4 a) (* b b)))
120.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
116.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
72.0ms
(fma c (* -4 a) (* b b))

simplify14.2s

Counts
225 → 191
Calls
225 calls:
Slowest
565.0ms
(/ (/ (* (* (- (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))
374.0ms
(/ (/ (* (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)))
231.0ms
(/ (* (* (/ (- (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))
225.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
205.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))

prune1.9s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 42.1b

localize62.0ms

Local error

Found 4 expressions with local error:

45.0b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.2b
(fma c (* -4 a) (* b b))
0.2b
(fma c (* -4 a) (* b b))
0.1b
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)

rewrite21.0ms

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
16.0ms
(/ (/ (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))
1.0ms
(fma c (* -4 a) (* b b))
0.0ms
(fma c (* -4 a) (* b b))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
601.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
450.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
72.0ms
(fma c (* -4 a) (* b b))
57.0ms
(fma c (* -4 a) (* b b))

simplify9.8s

Counts
109 → 118
Calls
109 calls:
Slowest
497.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
393.0ms
(/ (/ (* (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)))
307.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
303.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
260.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune1.7s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 42.0b

localize46.0ms

Local error

Found 4 expressions with local error:

45.0b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
1.0b
(cbrt 2)
1.0b
(cbrt 2)
1.0b
(cbrt 2)

rewrite2.0ms

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 2)
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series402.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
402.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify652.0ms

Counts
15 → 59
Calls
15 calls:
Slowest
408.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
144.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
21.0ms
(/ 1 (* (cbrt 2) (cbrt 2)))
21.0ms
(/ 1 (* (cbrt 2) (cbrt 2)))
21.0ms
(/ 1 (* (cbrt 2) (cbrt 2)))

prune1.1s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 42.0b

localize83.0ms

Local error

Found 4 expressions with local error:

45.0b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
1.0b
(cbrt 2)
1.0b
(cbrt 2)
1.0b
(cbrt 2)

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 2)
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series388.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
387.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify568.0ms

Counts
12 → 59
Calls
12 calls:
Slowest
269.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
229.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
14.0ms
(cbrt (* (cbrt 2) (cbrt 2)))
8.0ms
(cbrt (* (cbrt 2) (cbrt 2)))
8.0ms
(cbrt (* (cbrt 2) (cbrt 2)))

prune719.0ms

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 42.0b

regimes968.0ms

Accuracy

0% (2.9b remaining)

Error of 43.6b against oracle of 40.6b and baseline of 43.6b

bsearch7.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
1.8s4842×body160valid
1.1s8280×body80nan
1.0s16280×pre80true
989.0ms1419×body320valid
280.0ms1739×body80valid