Details

Time bar (total: 48.1s)

sample394.0ms

Algorithm
intervals
Results
91.0ms554×pre80true
56.0ms111×body320valid
47.0ms298×body80nan
33.0ms100×body160valid
9.0ms13×body640valid
7.0ms32×body80valid

simplify190.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
189.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize36.0ms

Local error

Found 4 expressions with local error:

29.4b
(- (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)))

rewrite43.0ms

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
22.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
9.0ms
(- (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))

series421.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
107.0ms
(sqrt (fma c (* -4 a) (* b b)))
102.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
92.0ms
(fma c (* -4 a) (* b b))

simplify15.3s

Counts
225 → 191
Calls
225 calls:
Slowest
564.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) (sqrt 2)) (sqrt a))
472.0ms
(/ (/ (* (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)))
252.0ms
(/ (* (* (/ (- (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))
214.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
194.0ms
(/ (/ (* (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

27 alts after pruning (27 fresh and 0 done)

Merged error: 49.1b

localize27.0ms

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 (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))

rewrite18.0ms

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
14.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
0.0ms
(fma c (* -4 a) (* b b))
0.0ms
(fma c (* -4 a) (* b b))
0.0ms
(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
619.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
392.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
96.0ms
(fma c (* -4 a) (* b b))
83.0ms
(fma c (* -4 a) (* b b))

simplify9.9s

Counts
109 → 118
Calls
109 calls:
Slowest
458.0ms
(/ (/ (* (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)))
414.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
337.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
244.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
213.0ms
(/ (/ (* (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)))

prune1.3s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 48.9b

localize71.0ms

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))
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))

series395.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
394.0ms
(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)

simplify579.0ms

Counts
15 → 59
Calls
15 calls:
Slowest
312.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
191.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
13.0ms
(/ 1 (* (cbrt 2) (cbrt 2)))
13.0ms
(/ 1 (* (cbrt 2) (cbrt 2)))
10.0ms
(/ 1 (* (cbrt 2) (cbrt 2)))

prune1.2s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 48.9b

localize75.0ms

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
13×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef
1×cbrt-div pow1/3 div-inv
Counts
4 → 58
Calls
4 calls:
Slowest
3.0ms
(cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2))
1.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
1.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
1.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
659.0ms
(cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2))
467.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
436.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
407.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

simplify4.1s

Counts
26 → 70
Calls
26 calls:
Slowest
699.0ms
(- (* (cbrt 1/2) (pow (* b -1) 1/3)) (+ (* 5/216 (* (/ (* (cbrt 1/2) (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 6)) (* a c)) (pow (/ 1 (pow b 2)) 1/3))) (* 1/3 (* (* (cbrt 1/2) (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2)) (pow (/ -1 (pow b 2)) 1/3)))))
660.0ms
(- (* (cbrt 1/2) (exp (* 1/3 (- (log -1) (log (/ 1 b)))))) (+ (* 1/3 (/ (* (cbrt 1/2) (* (exp (* 1/3 (- (log -1) (log (/ 1 b))))) (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2))) b)) (* 5/216 (* (/ (* (cbrt 1/2) (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 6)) (* a c)) (pow (/ 1 (pow b 2)) 1/3)))))
373.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
371.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
369.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune948.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 48.5b

regimes620.0ms

Accuracy

25% (2.3b remaining)

Error of 51.1b against oracle of 48.8b and baseline of 51.9b

bsearch30.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
1.7s3645×body320valid
1.6s16228×pre80true
1.2s8228×body80nan
992.0ms2970×body160valid
327.0ms494×body640valid
144.0ms891×body80valid