Details

Time bar (total: 30.9s)

sample155.0ms

Algorithm
intervals
Results
40.0ms124×body320valid
36.0ms501×pre80true
24.0ms245×body80nan
17.0ms84×body160valid
4.0ms10×body640valid
4.0ms38×body80valid

simplify136.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
136.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize43.0ms

Local error

Found 4 expressions with local error:

24.8b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.2b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
0.1b
(fma -3 (* c a) (* b b))
0.0b
(sqrt (fma -3 (* c a) (* b b)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff sqrt-prod
9×add-cbrt-cube add-exp-log
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod fma-udef div-inv
Counts
4 → 102
Calls
4 calls:
Slowest
40.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
16.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series395.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
105.0ms
(sqrt (fma -3 (* c a) (* b b)))
100.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
82.0ms
(fma -3 (* c a) (* b b))

simplify4.3s

Counts
87 → 114
Calls
87 calls:
Slowest
574.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
316.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
269.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))
205.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 3) 3) (* (* a a) a)))
128.0ms
(fma (* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b))))) (cbrt (sqrt (fma -3 (* c a) (* b b)))) (- (* b 1)))

prune1.5s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 48.7b

localize58.0ms

Local error

Found 4 expressions with local error:

51.0b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.2b
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.1b
(fma -3 (* c a) (* b b))
0.1b
(fma -3 (* c a) (* b b))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×times-frac fma-udef associate-/l*
2×cbrt-undiv div-exp
1×clear-num associate-/r* frac-2neg prod-exp cbrt-unprod div-inv
Counts
4 → 57
Calls
4 calls:
Slowest
20.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
1.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms
(fma -3 (* c a) (* b b))
0.0ms
(fma -3 (* c a) (* b b))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
591.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
430.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
80.0ms
(fma -3 (* c a) (* b b))
79.0ms
(fma -3 (* c a) (* b b))

simplify2.8s

Counts
24 → 69
Calls
24 calls:
Slowest
376.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
349.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/3 (/ b a)))
255.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/3 (/ b a)))
233.0ms
(/ (* (* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (* (* (* 3 3) 3) (* (* a a) a)))
206.0ms
(/ (* (* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune1.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 48.5b

localize117.0ms

Local error

Found 4 expressions with local error:

51.0b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
51.0b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
51.0b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.5b
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
7×cbrt-prod
6×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×times-frac fma-udef
1×cbrt-div pow1/3 div-inv
Counts
4 → 52
Calls
4 calls:
Slowest
7.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
1.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
572.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
426.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
410.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
405.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify3.5s

Counts
20 → 64
Calls
20 calls:
Slowest
619.0ms
(- (+ (* 5/162 (/ (* (cbrt -1/3) (* (exp (* 1/3 (+ (* 4 (log (/ -1 a))) (* 2 (log (/ -1 b)))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 6))) c)) (* (cbrt -1/3) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))))) (* 1/3 (/ (* (cbrt -1/3) (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2))) b)))
579.0ms
(- (* (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b))))) (cbrt 1/3)) (+ (* 5/162 (/ (* (cbrt 1/3) (* (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 6) (exp (* 1/3 (+ (* 2 (log (/ 1 b))) (* 4 (log (/ 1 a)))))))) c)) (* 1/3 (/ (* (cbrt 1/3) (* (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2))) b))))
326.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
290.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
285.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune1.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 48.1b

localize51.0ms

Local error

Found 4 expressions with local error:

51.0b
(fma (sqrt (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))
0.5b
(cbrt (fma -3 (* c a) (* b b)))
0.5b
(cbrt (fma -3 (* c a) (* b b)))
0.5b
(cbrt (fma -3 (* c a) (* b b)))

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 (fma -3 (* c a) (* b b)))
1.0ms
(cbrt (fma -3 (* c a) (* b b)))
1.0ms
(cbrt (fma -3 (* c a) (* b b)))
0.0ms
(fma (sqrt (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
709.0ms
(fma (sqrt (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))
321.0ms
(cbrt (fma -3 (* c a) (* b b)))
247.0ms
(cbrt (fma -3 (* c a) (* b b)))
214.0ms
(cbrt (fma -3 (* c a) (* b b)))

simplify2.7s

Counts
21 → 65
Calls
21 calls:
Slowest
326.0ms
(- (* (exp (* 1/3 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) (exp (* 1/6 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a))))))) b)
308.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
249.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
239.0ms
(- (* (exp (* 1/6 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) (exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))) b)
229.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune852.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 48.1b

regimes870.0ms

Accuracy

0% (3.2b remaining)

Error of 51.5b against oracle of 48.4b and baseline of 51.5b

bsearch6.0ms

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.0s3662×body320valid
1.5s8031×body80nan
891.0ms16031×pre80true
879.0ms2886×body160valid
379.0ms489×body640valid
111.0ms963×body80valid