Details

Time bar (total: 3.7m)

sample151.0ms

Algorithm
intervals
Results
37.0ms38×body2560valid
33.0ms34×body1280valid
29.0ms182×body80valid
14.0ms98×body80nan
7.0ms11×body640valid
7.0ms12×body320valid
3.0ms3×body5120valid
1.0ms4×body160valid

simplify207.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
207.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize25.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (fma (* a c) -4 (* b b)))
1.6b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.2b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
21×distribute-lft-neg-in
10×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×diff-log div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef flip-- associate-/l/
Counts
4 → 240
Calls
4 calls:
Slowest
29.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
20.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series420.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
112.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
107.0ms
(sqrt (fma (* a c) -4 (* b b)))
74.0ms
(fma (* a c) -4 (* b b))

simplify30.8s

Counts
334 → 252
Calls
334 calls:
Slowest
443.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
243.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
241.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (sqrt a))
234.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
232.0ms
(fma 1 (- b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))

prune3.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.8b

localize24.0ms

Local error

Found 3 expressions with local error:

22.3b
(sqrt (fma c (* -4 a) (* b b)))
1.6b
(+ (sqrt (fma c (* -4 a) (* b b))) b)
0.1b
(/ (/ (+ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) 0) 2) a)

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
155×*-un-lft-identity
138×times-frac
70×add-sqr-sqrt
69×add-cube-cbrt
49×distribute-lft-out
24×distribute-rgt-neg-in
22×associate-/l*
8×add-cbrt-cube add-exp-log
6×fma-def sqrt-prod
5×div-inv add-log-exp
4×pow1
3×expm1-log1p-u cbrt-undiv associate-/r* div-exp insert-posit16 log1p-expm1-u
2×div-sub
1×neg-sub0 +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-+l- flip-+ associate-/l/
Counts
3 → 147
Calls
3 calls:
Slowest
201.0ms
(/ (/ (+ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) 0) 2) a)
12.0ms
(+ (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series334.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
114.0ms
(/ (/ (+ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) 0) 2) a)
113.0ms
(sqrt (fma c (* -4 a) (* b b)))
106.0ms
(+ (sqrt (fma c (* -4 a) (* b b))) b)

simplify19.9s

Counts
182 → 156
Calls
182 calls:
Slowest
499.0ms
(/ (/ (* (cbrt (+ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) 0)) (cbrt (+ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) 0))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
490.0ms
(/ (/ (cbrt (+ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) 0)) (cbrt 2)) a)
316.0ms
(/ (/ (* (cbrt (+ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) 0)) (cbrt (+ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) 0))) (* (cbrt 2) (cbrt 2))) (sqrt a))
288.0ms
(/ (/ (+ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) 0) (cbrt 2)) (cbrt a))
242.0ms
(/ (/ (+ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) 0) (cbrt 2)) a)

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.8b

localize46.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (fma (* a c) -4 (* b b)))
1.6b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.2b
(fma (* a c) -4 (* b b))
0.1b
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
792×times-frac
512×add-sqr-sqrt
511×*-un-lft-identity
363×add-cube-cbrt
80×associate-/r*
74×distribute-lft-out-- difference-of-squares
70×sqrt-prod
60×prod-diff
58×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
17×div-inv
15×div-exp
13×add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×pow1 cbrt-undiv
5×associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp associate-/l*
2×diff-log
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef pow-flip flip-- inv-pow
Counts
4 → 469
Calls
4 calls:
Slowest
29.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
11.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series493.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
161.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
142.0ms
(sqrt (fma (* a c) -4 (* b b)))
106.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
85.0ms
(fma (* a c) -4 (* b b))

simplify2.3m

Counts
724 → 481
Calls
724 calls:
Slowest
831.0ms
(/ (cbrt 1) (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
724.0ms
(/ (sqrt 1) (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (cbrt 2))))
644.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ 1 (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2)))))
613.0ms
(/ 1 (/ 1 (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (sqrt 2))))
605.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (- (- b) (sqrt (fma (* a c) -4 (* b b))))))

prune5.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize46.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (fma (* a c) -4 (* b b)))
22.3b
(sqrt (fma (* a c) -4 (* b b)))
22.3b
(sqrt (fma (* a c) -4 (* b b)))
1.6b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
40×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip--
Counts
4 → 139
Calls
4 calls:
Slowest
22.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(sqrt (fma (* a c) -4 (* b b)))
99.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
89.0ms
(sqrt (fma (* a c) -4 (* b b)))
79.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify11.5s

Counts
162 → 151
Calls
162 calls:
Slowest
243.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
219.0ms
(fma (- (sqrt b)) (sqrt b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
212.0ms
(fma -1 b (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
208.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
197.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))

prune2.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.8b

regimes470.0ms

Accuracy

84.5% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 33.3b

bsearch155.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.4s1118×body2560valid
1.2s5818×body80valid
568.0ms869×body1280valid
344.0ms2866×body80nan
290.0ms443×body640valid
168.0ms118×body5120valid
89.0ms245×body320valid
26.0ms106×body160valid