Details

Time bar (total: 45.4s)

sample152.0ms

Algorithm
intervals
Results
35.0ms156×body160valid
32.0ms34×body320valid
27.0ms262×body80nan
25.0ms518×pre80true
7.0ms66×body80valid

simplify169.0ms

Calls
1 calls:
Slowest
168.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

localize19.0ms

Local error

Found 4 expressions with local error:

39.3b
(- (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))
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite30.0ms

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/
Calls
4 calls:
Slowest
16.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
9.0ms
(- (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))

series467.0ms

Calls
4 calls:
Slowest
143.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
127.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
113.0ms
(sqrt (fma c (* -4 a) (* b b)))
85.0ms
(fma c (* -4 a) (* b b))

simplify13.1s

Calls
225 calls:
Slowest
405.0ms
(/ (/ (* (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)))
192.0ms
(/ (* (* (/ (- (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))
178.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
172.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
155.0ms
(/ (/ (* (* (- (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))

prune2.2s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 40.1b

localize60.0ms

Local error

Found 4 expressions with local error:

42.9b
(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))

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/
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))

series1.1s

Calls
4 calls:
Slowest
503.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
430.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
78.0ms
(fma c (* -4 a) (* b b))
60.0ms
(fma c (* -4 a) (* b b))

simplify9.5s

Calls
109 calls:
Slowest
450.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
445.0ms
(/ (/ (* (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)))
368.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
274.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
221.0ms
(/ (/ (* (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)))

prune1.8s

Pruning

40 alts after pruning (40 fresh and 0 done)

Merged error: 40.0b

localize64.0ms

Local error

Found 4 expressions with local error:

42.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.5b
(cbrt a)
0.5b
(cbrt a)
0.5b
(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
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))

series1.6s

Calls
4 calls:
Slowest
603.0ms
(cbrt a)
445.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
302.0ms
(cbrt a)
249.0ms
(cbrt a)

simplify1.1s

Calls
21 calls:
Slowest
326.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
187.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
156.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
148.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
146.0ms
(* (pow (* a -1) 1/3) (cbrt -1))

prune1.3s

Pruning

47 alts after pruning (47 fresh and 0 done)

Merged error: 40.0b

localize95.0ms

Local error

Found 4 expressions with local error:

42.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.6b
(cbrt (cbrt a))
0.6b
(cbrt (cbrt a))
0.6b
(cbrt (cbrt a))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
27×cbrt-prod
10×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
Calls
4 calls:
Slowest
2.0ms
(cbrt (cbrt a))
2.0ms
(cbrt (cbrt a))
2.0ms
(cbrt (cbrt a))
1.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series1.7s

Calls
4 calls:
Slowest
437.0ms
(cbrt (cbrt a))
436.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
401.0ms
(cbrt (cbrt a))
393.0ms
(cbrt (cbrt a))

simplify2.7s

Calls
30 calls:
Slowest
701.0ms
(* (pow (* a -1) 1/9) (pow (cbrt -1) 1/3))
666.0ms
(* (pow (* a -1) 1/9) (pow (cbrt -1) 1/3))
602.0ms
(* (pow (* a -1) 1/9) (pow (cbrt -1) 1/3))
356.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
225.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune1.3s

Pruning

50 alts after pruning (50 fresh and 0 done)

Merged error: 40.0b

regimes1.3s

Accuracy

0% (3.0b remaining)

Error of 43.3b against oracle of 40.4b and baseline of 43.3b

bsearch6.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
1.6s4865×body160valid
1.3s8248×body80nan
1.1s16248×pre80true
627.0ms1348×body320valid
311.0ms1787×body80valid