Details

Time bar (total: 46.4s)

sample703.0ms

Algorithm
intervals
Results
69.0ms90×body160valid
38.0ms115×body320valid
26.0ms518×pre80true
26.0ms262×body80nan
8.0ms18×body640valid
3.0ms33×body80valid

simplify154.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.3b

localize41.0ms

Local error

Found 4 expressions with local error:

26.2b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b
(fma c (* -4 a) (* b b))
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.0b
(sqrt (fma c (* -4 a) (* b b)))

rewrite51.0ms

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)
17.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series509.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
143.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
135.0ms
(sqrt (fma c (* -4 a) (* b b)))
86.0ms
(fma c (* -4 a) (* b b))

simplify15.0s

Counts
225 → 191
Calls
225 calls:
Slowest
470.0ms
(/ (/ (* (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)))
253.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
200.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
195.0ms
(/ (* (* (/ (- (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))
169.0ms
(/ (/ (- (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (cbrt 2)) (sqrt a))

prune2.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 49.1b

localize33.0ms

Local error

Found 4 expressions with local error:

51.5b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.1b
(fma c (* -4 a) (* b b))
0.1b
(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)

rewrite28.0ms

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
613.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
444.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
73.0ms
(fma c (* -4 a) (* b b))
67.0ms
(fma c (* -4 a) (* b b))

simplify9.7s

Counts
109 → 118
Calls
109 calls:
Slowest
463.0ms
(/ (/ (* (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)))
401.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
307.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
254.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
238.0ms
(/ (/ (* (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)))

prune1.7s

Pruning

39 alts after pruning (39 fresh and 0 done)

Merged error: 48.9b

localize77.0ms

Local error

Found 4 expressions with local error:

51.5b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.6b
(cbrt a)
0.6b
(cbrt a)
0.6b
(cbrt a)

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
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))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
406.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
311.0ms
(cbrt a)
292.0ms
(cbrt a)
279.0ms
(cbrt a)

simplify983.0ms

Counts
21 → 65
Calls
21 calls:
Slowest
310.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
178.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
157.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
120.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
96.0ms
(* (pow (* a -1) 1/3) (cbrt -1))

prune1.2s

Pruning

42 alts after pruning (42 fresh and 0 done)

Merged error: 48.9b

localize82.0ms

Local error

Found 4 expressions with local error:

51.5b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.6b
(cbrt a)
0.6b
(cbrt a)
0.6b
(cbrt a)

rewrite5.0ms

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))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
422.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
254.0ms
(cbrt a)
234.0ms
(cbrt a)
219.0ms
(cbrt a)

simplify1.1s

Counts
21 → 65
Calls
21 calls:
Slowest
335.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
222.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
134.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
124.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
123.0ms
(* (pow (* a -1) 1/3) (cbrt -1))

prune1.1s

Pruning

44 alts after pruning (44 fresh and 0 done)

Merged error: 48.9b

regimes1.8s

Accuracy

0% (2.6b remaining)

Error of 52.1b against oracle of 49.4b and baseline of 52.1b

bsearch5.0ms

end0.0ms

sample6.3s

Algorithm
intervals
Results
1.8s3681×body320valid
1.6s8277×body80nan
1.2s16277×pre80true
951.0ms2934×body160valid
326.0ms524×body640valid
115.0ms861×body80valid