Details

Time bar (total: 1.3m)

sample104.0ms

Algorithm
intervals
Results
34.0ms41×body2560valid
23.0ms189×body80valid
13.0ms25×body1280valid
9.0ms91×body80nan
5.0ms11×body640valid
5.0ms10×body320valid
1.0ms4×body160valid

simplify136.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
136.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize47.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (- (* b b) (* (* c a) 4)))
1.3b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.8b
(- (* b b) (* (* c a) 4))
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- insert-posit16 flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 76
Calls
4 calls:
Slowest
83.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
63.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
19.0ms
(- (* b b) (* (* c a) 4))
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
93.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
82.0ms
(sqrt (- (* b b) (* (* c a) 4)))
49.0ms
(- (* b b) (* (* c a) 4))

simplify13.0s

Counts
105 → 88
Calls
105 calls:
Slowest
620.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
489.0ms
(- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4)))
402.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
386.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
374.0ms
(sqrt (+ (* (* b b) (* b b)) (+ (* (* (* c a) 4) (* (* c a) 4)) (* (* b b) (* (* c a) 4)))))

prune998.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize23.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (+ (* b b) (* (* c -4) a)))
1.3b
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
0.8b
(+ (* b b) (* (* c -4) a))
0.1b
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×insert-posit16
3×distribute-lft-out--
2×cbrt-undiv flip3-+ flip3-- sqrt-div div-exp flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 75
Calls
4 calls:
Slowest
84.0ms
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))
52.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
16.0ms
(+ (* b b) (* (* c -4) a))
6.0ms
(sqrt (+ (* b b) (* (* c -4) a)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
133.0ms
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))
124.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
58.0ms
(+ (* b b) (* (* c -4) a))

simplify9.7s

Counts
103 → 87
Calls
103 calls:
Slowest
951.0ms
(- (* (sqrt (+ (* b b) (* (* c -4) a))) (sqrt (+ (* b b) (* (* c -4) a)))) (* b b))
482.0ms
(exp (+ (* b b) (* (* c -4) a)))
426.0ms
(- (* (* b b) (* b b)) (* (* (* c -4) a) (* (* c -4) a)))
425.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c -4) a) (* (* c -4) a))))
322.0ms
(- (pow (sqrt (+ (* b b) (* (* c -4) a))) 3) (pow b 3))

prune937.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize32.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (+ (* b b) (* (* c -4) a)))
1.3b
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
0.8b
(+ (* b b) (* (* c -4) a))
0.2b
(/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
47×add-sqr-sqrt
36×*-un-lft-identity
26×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×associate-/r* div-exp
10×difference-of-squares
9×associate-/r/
8×sqrt-prod add-log-exp
6×pow1
5×cbrt-undiv flip3-- div-inv flip-- distribute-lft-out--
4×insert-posit16
3×rec-exp 1-exp prod-exp associate-/l*
2×flip3-+ sqrt-div flip-+
1×+-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log cbrt-unprod pow-flip inv-pow
Counts
4 → 121
Calls
4 calls:
Slowest
78.0ms
(/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))
44.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
15.0ms
(+ (* b b) (* (* c -4) a))
6.0ms
(sqrt (+ (* b b) (* (* c -4) a)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))
99.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
97.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
82.0ms
(+ (* b b) (* (* c -4) a))

simplify26.1s

Counts
177 → 133
Calls
177 calls:
Slowest
1.1s
(* (* (/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b))) (/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))) (/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b))))
1.0s
(- (* (sqrt (+ (* b b) (* (* c -4) a))) (sqrt (+ (* b b) (* (* c -4) a)))) (* b b))
594.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 2 a) (- (pow (sqrt (+ (* b b) (* (* c -4) a))) 3) (pow b 3))))
560.0ms
(exp (+ (* b b) (* (* c -4) a)))
483.0ms
(+ (pow (* b b) 3) (pow (* (* c -4) a) 3))

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

localize26.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (+ (* b b) (* (* a c) -4)))
1.3b
(- (sqrt (+ (* b b) (* (* a c) -4))) b)
0.8b
(+ (* b b) (* (* a c) -4))
0.2b
(* (/ 1/2 a) (- (sqrt (+ (* b b) (* (* a c) -4))) b))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
17×*-un-lft-identity
13×associate-*l* add-cube-cbrt
10×times-frac
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×pow1
6×associate-*r*
5×sqrt-prod
4×insert-posit16 difference-of-squares
3×sub-neg flip3-- flip--
2×distribute-rgt-in frac-times distribute-lft-in flip3-+ sqrt-div prod-exp associate-*r/ cbrt-unprod flip-+ distribute-lft-out-- unswap-sqr
1×cbrt-undiv +-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 88
Calls
4 calls:
Slowest
114.0ms
(* (/ 1/2 a) (- (sqrt (+ (* b b) (* (* a c) -4))) b))
41.0ms
(- (sqrt (+ (* b b) (* (* a c) -4))) b)
12.0ms
(sqrt (+ (* b b) (* (* a c) -4)))
8.0ms
(+ (* b b) (* (* a c) -4))

series454.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(* (/ 1/2 a) (- (sqrt (+ (* b b) (* (* a c) -4))) b))
120.0ms
(- (sqrt (+ (* b b) (* (* a c) -4))) b)
77.0ms
(sqrt (+ (* b b) (* (* a c) -4)))
76.0ms
(+ (* b b) (* (* a c) -4))

simplify14.4s

Counts
115 → 100
Calls
115 calls:
Slowest
909.0ms
(- (* (sqrt (+ (* b b) (* (* a c) -4))) (sqrt (+ (* b b) (* (* a c) -4)))) (* b b))
612.0ms
(* 1/2 (- (* (sqrt (+ (* b b) (* (* a c) -4))) (sqrt (+ (* b b) (* (* a c) -4)))) (* b b)))
530.0ms
(exp (+ (* b b) (* (* a c) -4)))
495.0ms
(+ (pow (* b b) 3) (pow (* (* a c) -4) 3))
477.0ms
(sqrt (+ (pow (* b b) 3) (pow (* (* a c) -4) 3)))

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.2b

regimes400.0ms

Accuracy

87% (3.6b remaining)

Error of 9.2b against oracle of 5.7b and baseline of 33.1b

bsearch346.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
983.0ms5869×body80valid
936.0ms1061×body2560valid
899.0ms2830×body80nan
676.0ms877×body1280valid
250.0ms439×body640valid
133.0ms103×body5120valid
117.0ms239×body320valid
33.0ms116×body160valid