Details

Time bar (total: 2.8m)

sample287.0ms

Algorithm
intervals
Results
37.0ms210×body80valid
25.0ms28×body2560valid
21.0ms27×body1280valid
13.0ms98×body80nan
8.0ms13×body640valid
2.0ms4×body320valid
1.0ms1×body5120valid
0.0ms1×body160valid

simplify125.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
125.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize37.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (- (* b_2 b_2) (* a c)))
1.2b
(- (* b_2 b_2) (* a c))
0.4b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 122
Calls
4 calls:
Slowest
75.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
47.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
28.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(- (* b_2 b_2) (* a c))

series367.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
110.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
103.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
102.0ms
(sqrt (- (* b_2 b_2) (* a c)))
53.0ms
(- (* b_2 b_2) (* a c))

simplify6.8s

Counts
116 → 134
Calls
116 calls:
Slowest
947.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
400.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
334.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
298.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
278.0ms
(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

localize18.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (- (* b_2 b_2) (* a c)))
4.9b
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
1.2b
(- (* b_2 b_2) (* a c))
0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
481×times-frac
378×add-sqr-sqrt
366×*-un-lft-identity
358×add-cube-cbrt
287×prod-diff
143×sqrt-prod
39×div-inv
23×fma-neg
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- sqrt-div insert-posit16 log1p-expm1-u flip-- distribute-lft-out--
3×associate-/r*
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-exp frac-sub sub-div
Counts
4 → 415
Calls
4 calls:
Slowest
74.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
18.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series450.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
129.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))
59.0ms
(- (* b_2 b_2) (* a c))

simplify2.1m

Counts
687 → 427
Calls
687 calls:
Slowest
715.0ms
(fma (/ (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (* (cbrt a) (cbrt a))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (cbrt a)) (- (* (cbrt (/ b_2 a)) (* (cbrt (/ b_2 a)) (cbrt (/ b_2 a))))))
691.0ms
(fma (/ (sqrt 1) (* (cbrt a) (cbrt a))) (/ (sqrt (- (* b_2 b_2) (* a c))) (cbrt a)) (- (* (/ (sqrt b_2) a) (/ (sqrt b_2) 1))))
670.0ms
(fma (/ 1 (* (cbrt a) (cbrt a))) (/ (sqrt (- (* b_2 b_2) (* a c))) (cbrt a)) (- (* (/ (sqrt b_2) a) (/ (sqrt b_2) 1))))
615.0ms
(fma (- (/ b_2 (cbrt a))) (/ 1 (* (cbrt a) (cbrt a))) (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a)))))
611.0ms
(fma (- (/ b_2 (cbrt a))) (/ 1 (* (cbrt a) (cbrt a))) (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a)))))

prune4.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

localize25.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (- (* b_2 b_2) (* a c)))
20.2b
(sqrt (- (* b_2 b_2) (* a c)))
10.5b
(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)) (/ b_2 a))
1.2b
(- (* b_2 b_2) (* a c))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
14×prod-diff
13×*-un-lft-identity add-cube-cbrt
12×sqrt-div
9×times-frac
8×add-log-exp
6×pow1 flip3-- sqrt-prod flip--
5×frac-sub
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×frac-times rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*l/ associate-*r/
1×div-inv sub-div
Counts
4 → 88
Calls
4 calls:
Slowest
64.0ms
(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)) (/ b_2 a))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))
16.0ms
(- (* b_2 b_2) (* a c))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)) (/ b_2 a))
85.0ms
(sqrt (- (* b_2 b_2) (* a c)))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))
67.0ms
(- (* b_2 b_2) (* a c))

simplify9.8s

Counts
68 → 100
Calls
68 calls:
Slowest
718.0ms
(/ (exp (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a))) (exp (/ b_2 a)))
498.0ms
(fma (- (/ b_2 (cbrt a))) (/ 1 (* (cbrt a) (cbrt a))) (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a)))))
424.0ms
(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a) (- (* (/ (cbrt b_2) a) (/ (* (cbrt b_2) (cbrt b_2)) 1))))
400.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
361.0ms
(* (sqrt (sqrt (+ (* (* b_2 b_2) (* b_2 b_2)) (+ (* (* a c) (* a c)) (* (* b_2 b_2) (* a c)))))) a)

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.6b

localize57.0ms

Local error

Found 4 expressions with local error:

21.0b
(cbrt (- (* b_2 b_2) (* a c)))
21.0b
(cbrt (- (* b_2 b_2) (* a c)))
21.0b
(cbrt (- (* b_2 b_2) (* a c)))
20.2b
(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 101
Calls
4 calls:
Slowest
128.0ms
(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
6.0ms
(cbrt (- (* b_2 b_2) (* a c)))
5.0ms
(cbrt (- (* b_2 b_2) (* a c)))
5.0ms
(cbrt (- (* b_2 b_2) (* a c)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(cbrt (- (* b_2 b_2) (* a c)))
124.0ms
(cbrt (- (* b_2 b_2) (* a c)))
113.0ms
(cbrt (- (* b_2 b_2) (* a c)))
79.0ms
(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))

simplify10.6s

Counts
69 → 113
Calls
69 calls:
Slowest
479.0ms
(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))) (cbrt (- (* b_2 b_2) (* a c)))))
472.0ms
(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))))
424.0ms
(sqrt (* (* (cbrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3))) (cbrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))) (cbrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))))
424.0ms
(sqrt (* (* (cbrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3))) (cbrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))) (cbrt (- (* b_2 b_2) (* a c)))))
418.0ms
(sqrt (* (* (cbrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.6b

regimes296.0ms

Accuracy

79.3% (5.7b remaining)

Error of 11.3b against oracle of 5.6b and baseline of 33.2b

bsearch165.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
915.0ms1077×body2560valid
910.0ms879×body1280valid
793.0ms5901×body80valid
289.0ms471×body640valid
288.0ms2886×body80nan
134.0ms217×body320valid
98.0ms95×body5120valid
25.0ms113×body160valid