Details

Time bar (total: 2.9m)

sample150.0ms

Algorithm
intervals
Results
56.0ms43×body2560valid
26.0ms174×body80valid
21.0ms30×body1280valid
12.0ms81×body80nan
10.0ms17×body640valid
3.0ms7×body320valid
1.0ms3×body160valid
1.0ms1×body5120valid

simplify270.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
270.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize45.0ms

Local error

Found 4 expressions with local error:

22.7b
(sqrt (fma (* a c) -4 (* b b)))
1.6b
(fma (* a c) -4 (* b b))
1.0b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite51.0ms

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
35.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
10.0ms
(- (- 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))

series419.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
101.0ms
(sqrt (fma (* a c) -4 (* b b)))
91.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
76.0ms
(fma (* a c) -4 (* b b))

simplify29.3s

Counts
334 → 252
Calls
334 calls:
Slowest
384.0ms
(/ (/ (* (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)))
263.0ms
(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))))))))
254.0ms
(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))))))))
243.0ms
(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))))))))
241.0ms
(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))))))))

prune3.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

localize45.0ms

Local error

Found 4 expressions with local error:

22.7b
(sqrt (fma a (* c -4) (* b b)))
1.0b
(+ b (sqrt (fma a (* c -4) (* b b))))
0.2b
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
0.0b
(fma a (* c -4) (* b b))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
16×add-cube-cbrt
13×associate-*r*
12×associate-*l*
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
6×add-log-exp
4×distribute-lft-neg-in expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u distribute-neg-frac
3×fma-def flip3-+ sqrt-prod flip-+ distribute-lft-out
2×frac-times associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×distribute-lft-neg-out cbrt-undiv +-commutative rem-sqrt-square neg-mul-1 sum-log sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv
Counts
4 → 94
Calls
4 calls:
Slowest
52.0ms
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
7.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
3.0ms
(sqrt (fma a (* c -4) (* b b)))
0.0ms
(fma a (* c -4) (* b b))

series480.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
137.0ms
(sqrt (fma a (* c -4) (* b b)))
135.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
71.0ms
(fma a (* c -4) (* b b))

simplify3.9s

Counts
58 → 106
Calls
58 calls:
Slowest
347.0ms
(* (* (* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)))
312.0ms
(* (+ (* b b) (- (* (sqrt (fma a (* c -4) (* b b))) (sqrt (fma a (* c -4) (* b b)))) (* b (sqrt (fma a (* c -4) (* b b)))))) a)
264.0ms
(* (- (+ (pow b 3) (pow (sqrt (fma a (* c -4) (* b b))) 3))) (/ 1/2 a))
247.0ms
(* (* (* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (* (* (/ 1/2 a) (/ 1/2 a)) (/ 1/2 a)))
234.0ms
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

localize38.0ms

Local error

Found 4 expressions with local error:

22.7b
(sqrt (fma (* a c) -4 (* b b)))
1.6b
(fma (* a c) -4 (* b b))
1.0b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite55.0ms

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
20.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
19.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series453.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
132.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
103.0ms
(sqrt (fma (* a c) -4 (* b b)))
76.0ms
(fma (* a c) -4 (* b b))

simplify1.9m

Counts
724 → 481
Calls
724 calls:
Slowest
815.0ms
(/ (cbrt 1) (/ (sqrt a) (/ (- (sqrt (- b)) (sqrt (sqrt (fma (* a c) -4 (* b b))))) (cbrt 2))))
597.0ms
(/ 1 (/ (* (cbrt a) (cbrt a)) (/ (+ (sqrt (- b)) (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt 2))))
594.0ms
(/ (sqrt 1) (/ (cbrt a) (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
502.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (- (- b) (sqrt (fma (* a c) -4 (* b b))))))
490.0ms
(/ (cbrt 1) (/ (sqrt a) (/ (- (sqrt (- b)) (sqrt (sqrt (fma (* a c) -4 (* b b))))) (cbrt 2))))

prune4.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.6b

localize28.0ms

Local error

Found 4 expressions with local error:

22.7b
(sqrt (fma c (* -4 a) (* b b)))
1.0b
(/ 1 (sqrt 2))
1.0b
(- (- b) (sqrt (fma c (* -4 a) (* b b))))
0.5b
(* a (sqrt 2))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
68×*-un-lft-identity
64×add-cube-cbrt
60×prod-diff
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
18×times-frac
10×fma-neg add-exp-log
9×pow1
8×add-cbrt-cube add-log-exp
7×neg-mul-1
6×associate-/r* associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*l* pow-flip associate-/l*
2×sqrt-pow1 pow1/2 diff-log div-exp distribute-lft-out-- difference-of-squares unswap-sqr
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp clear-num sub-neg frac-2neg flip3-- 1-exp pow-prod-down neg-log prod-exp *-commutative cbrt-unprod div-inv flip-- inv-pow
Counts
4 → 180
Calls
4 calls:
Slowest
15.0ms
(- (- b) (sqrt (fma c (* -4 a) (* b b))))
7.0ms
(* a (sqrt 2))
5.0ms
(/ 1 (sqrt 2))
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series192.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
77.0ms
(sqrt (fma c (* -4 a) (* b b)))
73.0ms
(- (- b) (sqrt (fma c (* -4 a) (* b b))))
42.0ms
(* a (sqrt 2))
0.0ms
(/ 1 (sqrt 2))

simplify8.7s

Counts
215 → 190
Calls
215 calls:
Slowest
195.0ms
(* (/ 1 (sqrt 2)) (/ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) (* a (sqrt 2))))
157.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))))))
148.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))))))
144.0ms
(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))))))
140.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))))))

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.6b

regimes299.0ms

Accuracy

83.6% (4.6b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 33.6b

bsearch164.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
747.0ms1091×body2560valid
603.0ms2809×body80nan
579.0ms5924×body80valid
490.0ms891×body1280valid
172.0ms426×body640valid
110.0ms107×body5120valid
79.0ms229×body320valid
17.0ms97×body160valid