Details

Time bar (total: 18.9s)

sample158.0ms

Algorithm
intervals
Results
38.0ms162×body160valid
32.0ms526×pre80true
31.0ms270×body80nan
25.0ms40×body320valid
7.0ms54×body80valid

simplify155.0ms

Calls
1 calls:
Slowest
155.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize27.0ms

Local error

Found 4 expressions with local error:

37.7b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.3b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
0.1b
(fma -3 (* c a) (* b b))
0.1b
(sqrt (fma -3 (* c a) (* b b)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube fma-neg add-exp-log sqrt-prod
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×times-frac associate-/l*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg pow1/2 div-sub div-exp fma-udef div-inv
Calls
4 calls:
Slowest
25.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
15.0ms
(- (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))

series229.0ms

Calls
4 calls:
Slowest
79.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
62.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
48.0ms
(sqrt (fma -3 (* c a) (* b b)))
40.0ms
(fma -3 (* c a) (* b b))

simplify1.8s

Calls
34 calls:
Slowest
478.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
217.0ms
(/ (* (* (- (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)))
179.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
144.0ms
(- (log (- (sqrt (fma -3 (* c a) (* b b))) b)) (log (* 3 a)))
68.0ms
(- (pow b 2) (* 3 (* a c)))

prune1.1s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 40.9b

localize16.0ms

Local error

Found 4 expressions with local error:

43.7b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.3b
(/ (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))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×times-frac fma-udef associate-/l*
1×cbrt-undiv clear-num associate-/r* frac-2neg div-exp div-inv
Calls
4 calls:
Slowest
4.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.0ms
(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))

series812.0ms

Calls
4 calls:
Slowest
424.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
308.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
47.0ms
(fma -3 (* c a) (* b b))
33.0ms
(fma -3 (* c a) (* b b))

simplify2.1s

Calls
22 calls:
Slowest
331.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
330.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/3 (/ b a)))
230.0ms
(/ (* (* (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)))
221.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
208.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/3 (/ b a)))

prune1.1s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 40.8b

localize7.0ms

Local error

Found 4 expressions with local error:

43.7b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.3b
(/ (* 3 a) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))
0.2b
(/ 1 (/ (* 3 a) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))))
0.1b
(fma -3 (* c a) (* b b))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-/r*
9×add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×times-frac add-cbrt-cube
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×rec-exp clear-num frac-2neg div-exp fma-udef
1×cbrt-undiv associate-/r/ pow-flip associate-/l* inv-pow
Calls
4 calls:
Slowest
3.0ms
(/ (* 3 a) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))
2.0ms
(/ 1 (/ (* 3 a) (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 -3 (* c a) (* b b))

series902.0ms

Calls
4 calls:
Slowest
314.0ms
(/ (* 3 a) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))
283.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
255.0ms
(/ 1 (/ (* 3 a) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))))
50.0ms
(fma -3 (* c a) (* b b))

simplify2.9s

Calls
32 calls:
Slowest
347.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
328.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/3 (/ b a)))
209.0ms
(/ (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* (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))))
204.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/3 (/ b a)))
204.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune1.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 5.7b

localize8.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ 1 (* -2 (/ b c)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log
1×add-sqr-sqrt expm1-log1p-u rec-exp clear-num associate-/r* frac-2neg *-un-lft-identity add-cbrt-cube associate-*r/ associate-/r/ add-cube-cbrt insert-posit16 log1p-expm1-u div-inv pow-flip inv-pow add-log-exp
Calls
1 calls:
Slowest
1.0ms
(/ 1 (* -2 (/ b c)))

series9.0ms

Calls
1 calls:
Slowest
9.0ms
(/ 1 (* -2 (/ b c)))

simplify64.0ms

Calls
5 calls:
Slowest
26.0ms
(* -1/2 (/ c b))
21.0ms
(* -1/2 (/ c b))
12.0ms
(* -1/2 (/ c b))
3.0ms
(- 1)
2.0ms
(/ b c)

prune146.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 5.6b

regimes623.0ms

Accuracy

0% (6.9b remaining)

Error of 12.1b against oracle of 5.1b and baseline of 12.1b

bsearch1.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
1.7s4807×body160valid
1.2s16072×pre80true
1.1s8072×body80nan
648.0ms1807×body80valid
562.0ms1386×body320valid