Details

Time bar (total: 25.9s)

sample279.0ms

Algorithm
intervals
Results
70.0ms292×body80nan
41.0ms113×body320valid
36.0ms548×pre80true
23.0ms103×body160valid
9.0ms18×body640valid
2.0ms22×body80valid

simplify110.0ms

Calls
1 calls:
Slowest
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.0b

localize21.0ms

Local error

Found 4 expressions with local error:

30.4b
(- (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)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×fma-neg sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×div-sub div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg flip3-- pow1/2 fma-udef flip-- associate-/l/
Calls
4 calls:
Slowest
22.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
17.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(fma c (* -4 a) (* b b))

series442.0ms

Calls
4 calls:
Slowest
133.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
126.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
92.0ms
(sqrt (fma c (* -4 a) (* b b)))
91.0ms
(fma c (* -4 a) (* b b))

simplify648.0ms

Calls
26 calls:
Slowest
78.0ms
(- (pow b 2) (* 4 (* a c)))
76.0ms
(- (pow b 2) (* 4 (* a c)))
63.0ms
(- (pow b 2) (* 4 (* a c)))
60.0ms
(sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
60.0ms
(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))

prune927.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 51.5b

localize31.0ms

Local error

Found 4 expressions with local error:

53.9b
(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)

rewrite13.0ms

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 associate-/l* add-log-exp
3×fma-udef
2×div-inv
1×clear-num frac-2neg associate-/l/
Calls
4 calls:
Slowest
11.0ms
(/ (/ (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

Calls
4 calls:
Slowest
649.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
433.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
80.0ms
(fma c (* -4 a) (* b b))
70.0ms
(fma c (* -4 a) (* b b))

simplify1.7s

Calls
16 calls:
Slowest
320.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
289.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
270.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
155.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
94.0ms
(* (cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2)) (cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2)))

prune894.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 51.3b

localize29.0ms

Local error

Found 4 expressions with local error:

53.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
53.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
53.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.4b
(cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×cbrt-prod 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
Calls
4 calls:
Slowest
2.0ms
(cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2))
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

Calls
4 calls:
Slowest
663.0ms
(cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2))
476.0ms
(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))
384.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

simplify3.6s

Calls
17 calls:
Slowest
589.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
547.0ms
(- (* (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)))))
431.0ms
(- (* (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)))))
389.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
355.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune996.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 50.8b

localize57.0ms

Local error

Found 4 expressions with local error:

53.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
53.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
3.1b
(exp (+ (log c) (log a)))
0.6b
(cbrt (/ (* -2 (exp (+ (log c) (log a)))) b))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
6×add-sqr-sqrt add-cube-cbrt
5×add-log-exp
4×cbrt-prod expm1-log1p-u pow1 exp-prod add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×fma-udef rem-exp-log
1×cbrt-div sum-log pow1/3 exp-sum div-inv distribute-lft-out
Calls
4 calls:
Slowest
10.0ms
(exp (+ (log c) (log a)))
5.0ms
(cbrt (/ (* -2 (exp (+ (log c) (log a)))) 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))

series1.3s

Calls
4 calls:
Slowest
440.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
430.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
317.0ms
(cbrt (/ (* -2 (exp (+ (log c) (log a)))) b))
128.0ms
(exp (+ (log c) (log a)))

simplify2.7s

Calls
23 calls:
Slowest
405.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
369.0ms
(exp (- (* 2 (log -1)) (+ (log (/ -1 c)) (log (/ -1 a)))))
316.0ms
(* (exp (* 1/3 (- (log (/ 1 b)) (+ (log (/ 1 a)) (log (/ 1 c)))))) (cbrt -2))
301.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
282.0ms
(* (cbrt -2) (exp (* 1/3 (- (+ (log a) (log c)) (log b)))))

prune1.7s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 50.7b

regimes1.2s

Accuracy

0% (3.8b remaining)

Error of 52.4b against oracle of 48.6b and baseline of 52.4b

bsearch10.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
1.6s3647×body320valid
1.4s2900×body160valid
1.2s8142×body80nan
995.0ms16142×pre80true
404.0ms518×body640valid
122.0ms935×body80valid