Details

Time bar (total: 55.0s)

sample114.0ms

Algorithm
intervals
Results
68.0ms278×body80valid
21.0ms98×body80nan

simplify265.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
265.0ms
(if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize175.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b b) (* (* 4 a) c)))
23.0b
(sqrt (- (* b b) (* (* 4 a) c)))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 155
Calls
4 calls:
Slowest
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
27.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
124.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
119.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
108.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify21.2s

Counts
172 → 167
Calls
172 calls:
Slowest
482.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
393.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (- (* b b) (* (* 4 a) c)))) (* (cbrt (sqrt (- (* b b) (* (* 4 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4 a) c))))))))
393.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
342.0ms
(fma 1 (- b) (- (* (cbrt (sqrt (- (* b b) (* (* 4 a) c)))) (* (cbrt (sqrt (- (* b b) (* (* 4 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4 a) c))))))))
327.0ms
(fma 1 (- b) (- (* (cbrt (sqrt (- (* b b) (* (* 4 a) c)))) (* (cbrt (sqrt (- (* b b) (* (* 4 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4 a) c))))))))

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize198.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b b) (* (* 4 a) c)))
3.6b
(* (/ c b) a)
3.4b
(/ (* 2 c) (* (- (* (/ c b) a) b) 2))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×add-cbrt-cube add-exp-log
20×*-un-lft-identity
16×add-cube-cbrt
13×associate-*l*
11×times-frac
10×fma-def
8×add-log-exp
7×pow1
6×prod-exp cbrt-unprod
5×cbrt-undiv div-exp
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in associate-*r* associate-*l/ sqrt-prod
2×sum-log flip3-- sqrt-div associate-/r/ div-inv flip-- distribute-lft-out unswap-sqr
1×neg-sub0 +-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 frac-2neg sqrt-pow1 flip3-+ pow1/2 pow-prod-down neg-log *-commutative associate-+l- flip-+ associate-/l*
Counts
4 → 107
Calls
4 calls:
Slowest
42.0ms
(/ (* 2 c) (* (- (* (/ c b) a) b) 2))
19.0ms
(* (/ c b) a)
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
245.0ms
(/ (* 2 c) (* (- (* (/ c b) a) b) 2))
119.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
105.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
25.0ms
(* (/ c b) a)

simplify9.6s

Counts
65 → 119
Calls
65 calls:
Slowest
2.2s
(/ (* (* (* 2 2) 2) (* (* c c) c)) (* (* (* (- (* (/ c b) a) b) 2) (* (- (* (/ c b) a) b) 2)) (* (- (* (/ c b) a) b) 2)))
1.0s
(/ (* (* (* 2 2) 2) (* (* c c) c)) (* (* (* (- (* (/ c b) a) b) (- (* (/ c b) a) b)) (- (* (/ c b) a) b)) (* (* 2 2) 2)))
888.0ms
(- (log (* 2 c)) (+ (log (- (* (/ c b) a) b)) (log 2)))
860.0ms
(/ (* (* (* 2 c) (* 2 c)) (* 2 c)) (* (* (* (- (* (/ c b) a) b) 2) (* (- (* (/ c b) a) b) 2)) (* (- (* (/ c b) a) b) 2)))
848.0ms
(/ (* (* (* 2 c) (* 2 c)) (* 2 c)) (* (* (* (- (* (/ c b) a) b) (- (* (/ c b) a) b)) (- (* (/ c b) a) b)) (* (* 2 2) 2)))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize190.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b b) (* (* 4 a) c)))
23.0b
(sqrt (- (* b b) (* (* 4 a) c)))
10.1b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
3.6b
(* (/ c b) a)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
17×*-un-lft-identity add-cube-cbrt
13×associate-*l*
10×fma-def times-frac
9×add-cbrt-cube add-exp-log
8×pow1 add-log-exp
6×sqrt-prod
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in distribute-rgt-neg-in associate-*r*
2×rem-sqrt-square sum-log sqrt-pow1 flip3-- pow1/2 prod-exp cbrt-unprod flip-- unswap-sqr
1×neg-sub0 cbrt-undiv +-commutative neg-mul-1 flip3-+ div-exp pow-prod-down neg-log associate-*l/ *-commutative associate-+l- flip-+ div-inv
Counts
4 → 97
Calls
4 calls:
Slowest
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
12.0ms
(* (/ c b) a)
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))

series378.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
114.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
101.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
38.0ms
(* (/ c b) a)

simplify4.1s

Counts
58 → 109
Calls
58 calls:
Slowest
411.0ms
(* (exp (- b)) (exp (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c)))))))
398.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
394.0ms
(* (/ 1 (exp b)) (exp (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c)))))))
330.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
260.0ms
(- b (* 2 (/ (* a c) b)))

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize169.0ms

Local error

Found 4 expressions with local error:

27.3b
(cbrt (* (* (* (/ c b) a) (* (/ c b) a)) (* (/ c b) a)))
23.0b
(sqrt (- (* b b) (* (* 4 a) c)))
3.6b
(* (/ c b) a)
3.6b
(* (/ c b) a)

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
26×associate-*l*
21×*-un-lft-identity add-cube-cbrt
20×times-frac
19×associate-*l/
14×add-cbrt-cube add-exp-log
9×pow1
7×cbrt-div
6×associate-*r*
5×frac-times
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-*r/ sqrt-prod
2×cbrt-undiv sqrt-div div-exp pow-prod-down *-commutative div-inv
1×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow1/3 pow3 rem-cbrt-cube flip--
Counts
4 → 108
Calls
4 calls:
Slowest
144.0ms
(cbrt (* (* (* (/ c b) a) (* (/ c b) a)) (* (/ c b) a)))
21.0ms
(* (/ c b) a)
21.0ms
(* (/ c b) a)
20.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
70.0ms
(cbrt (* (* (* (/ c b) a) (* (/ c b) a)) (* (/ c b) a)))
36.0ms
(* (/ c b) a)
35.0ms
(* (/ c b) a)

simplify5.0s

Counts
74 → 120
Calls
74 calls:
Slowest
387.0ms
(cbrt (* (* (* (/ c b) a) (* c a)) (* c a)))
373.0ms
(* -1 (/ (* a (* (cbrt -1) c)) b))
342.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
330.0ms
(cbrt (* (* (/ c b) a) (* (/ c b) a)))
330.0ms
(cbrt (* (* (* c a) (* c a)) (* (/ c b) a)))

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

regimes301.0ms

Accuracy

92.8% (1.1b remaining)

Error of 6.5b against oracle of 5.4b and baseline of 20.4b

bsearch325.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.1s8785×body80valid
431.0ms2882×body80nan