Details

Time bar (total: 50.5s)

sample689.0ms

Algorithm
intervals
Results
460.0ms235×body80nan
41.0ms130×body320valid
23.0ms491×pre80true
17.0ms81×body160valid
5.0ms12×body640valid
3.0ms33×body80valid

simplify157.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
156.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.9b

localize54.0ms

Local error

Found 4 expressions with local error:

24.3b
(- (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)))

rewrite62.0ms

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
33.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
18.0ms
(- (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))

series405.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
94.0ms
(fma c (* -4 a) (* b b))
92.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
80.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify14.0s

Counts
225 → 191
Calls
225 calls:
Slowest
384.0ms
(/ (/ (* (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)))
201.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
177.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) 1)
165.0ms
(/ (* (* (/ (- (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))) (sqrt 2)) (* (cbrt a) (cbrt a)))

prune2.4s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 48.7b

localize49.0ms

Local error

Found 4 expressions with local error:

51.2b
(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))

rewrite10.0ms

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
8.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
0.0ms
(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
667.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
415.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
81.0ms
(fma c (* -4 a) (* b b))
81.0ms
(fma c (* -4 a) (* b b))

simplify9.7s

Counts
109 → 118
Calls
109 calls:
Slowest
422.0ms
(/ (/ (* (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)))
384.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
314.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
283.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
214.0ms
(/ (/ (* (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: 48.5b

localize65.0ms

Local error

Found 4 expressions with local error:

51.2b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
51.2b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
51.2b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.5b
(cbrt (* (* (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
7×cbrt-div
5×frac-times associate-*l/
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r/ fma-udef
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 53
Calls
4 calls:
Slowest
44.0ms
(cbrt (* (* (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
668.0ms
(cbrt (* (* (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)))
419.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
399.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
382.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

simplify5.6s

Counts
21 → 65
Calls
21 calls:
Slowest
469.0ms
(cbrt (* (* (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a) (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2)) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)))
451.0ms
(cbrt (* (* (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)) (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2)))
446.0ms
(cbrt (* (* (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a) (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2)) (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2)))
443.0ms
(- (/ (* b (cbrt -1/8)) a) (/ (* (cbrt -1/8) (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2)) a))
424.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune1.1s

Pruning

39 alts after pruning (38 fresh and 1 done)

Merged error: 48.5b

localize95.0ms

Local error

Found 4 expressions with local error:

51.2b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
51.2b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
51.2b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
1.0b
(cbrt 2)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
5×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×cbrt-prod fma-udef
1×pow1/3
Counts
4 → 47
Calls
4 calls:
Slowest
1.0ms
(cbrt 2)
1.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series1.7s

Counts
4 → 10
Calls
4 calls:
Slowest
822.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
448.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
433.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(cbrt 2)

simplify1.8s

Counts
13 → 57
Calls
13 calls:
Slowest
402.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
344.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
337.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
230.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
221.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune721.0ms

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 48.5b

regimes931.0ms

Accuracy

0% (2.6b remaining)

Error of 51.5b against oracle of 48.9b and baseline of 51.5b

bsearch7.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
1.7s3623×body320valid
1.4s16234×pre80true
1.2s8234×body80nan
916.0ms2878×body160valid
308.0ms545×body640valid
181.0ms954×body80valid