Details

Time bar (total: 21.6s)

sample152.0ms

Algorithm
intervals
Results
55.0ms149×body160valid
31.0ms272×body80nan
30.0ms528×pre80true
13.0ms107×body80valid

simplify110.0ms

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize24.0ms

Local error

Found 4 expressions with local error:

29.6b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(fma c (* -4 a) (* b b))
0.2b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite19.0ms

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
11.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
6.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series192.0ms

Calls
4 calls:
Slowest
58.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
48.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
43.0ms
(fma c (* -4 a) (* b b))
43.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify640.0ms

Calls
26 calls:
Slowest
83.0ms
(- (pow b 2) (* 4 (* a c)))
76.0ms
(- (pow b 2) (* 4 (* a c)))
62.0ms
(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
58.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
56.0ms
(- (pow b 2) (* 4 (* a c)))

prune763.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 26.9b

localize15.0ms

Local error

Found 4 expressions with local error:

29.4b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.2b
(fma c (* -4 a) (* b b))
0.2b
(fma c (* -4 a) (* b b))
0.2b
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)

rewrite6.0ms

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
5.0ms
(/ (/ (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))

series755.0ms

Calls
4 calls:
Slowest
397.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
292.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
37.0ms
(fma c (* -4 a) (* b b))
30.0ms
(fma c (* -4 a) (* b b))

simplify1.7s

Calls
16 calls:
Slowest
346.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
332.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
199.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
199.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
114.0ms
(* (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)))

prune998.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 26.8b

localize31.0ms

Local error

Found 4 expressions with local error:

29.4b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
29.4b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
29.4b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.6b
(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))

series1.3s

Calls
4 calls:
Slowest
494.0ms
(cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2))
302.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
294.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
259.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

simplify3.1s

Calls
17 calls:
Slowest
586.0ms
(- (* (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)))))
407.0ms
(- (* (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)))))
371.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
327.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
294.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune958.0ms

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 26.6b

localize35.0ms

Local error

Found 4 expressions with local error:

29.4b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
29.4b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
29.4b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
29.4b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Calls
4 calls:
Slowest
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))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series1.1s

Calls
4 calls:
Slowest
323.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
285.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
259.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
239.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

simplify2.3s

Calls
12 calls:
Slowest
399.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
341.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
322.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
270.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
241.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune1.4s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 26.5b

regimes942.0ms

Accuracy

0% (3.1b remaining)

Error of 29.0b against oracle of 25.9b and baseline of 29.0b

bsearch10.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.6s4462×body160valid
1.2s8787×body80nan
1.1s16787×pre80true
644.0ms3538×body80valid