Details

Time bar (total: 1.2m)

sample152.0ms

Algorithm
intervals
Results
52.0ms41×body2560valid
29.0ms189×body80valid
19.0ms25×body1280valid
14.0ms91×body80nan
7.0ms11×body640valid
5.0ms10×body320valid
1.0ms4×body160valid

simplify426.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
426.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize48.0ms

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))

rewrite168.0ms

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
96.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
48.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms
(- (* b b) (* (* c a) 4))
8.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
106.0ms
(sqrt (- (* b b) (* (* c a) 4)))
101.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
50.0ms
(- (* b b) (* (* c a) 4))

simplify12.5s

Counts
105 → 88
Calls
105 calls:
Slowest
700.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
400.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
396.0ms
(- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4)))
395.0ms
(+ (* (* b b) (* b b)) (+ (* (* (* c a) 4) (* (* c a) 4)) (* (* b b) (* (* c a) 4))))
351.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize22.0ms

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))

rewrite145.0ms

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
83.0ms
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))
42.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
12.0ms
(+ (* b b) (* (* c -4) a))
7.0ms
(sqrt (+ (* b b) (* (* c -4) a)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
128.0ms
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))
101.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
72.0ms
(+ (* b b) (* (* c -4) a))

simplify8.9s

Counts
103 → 87
Calls
103 calls:
Slowest
988.0ms
(- (* (sqrt (+ (* b b) (* (* c -4) a))) (sqrt (+ (* b b) (* (* c -4) a)))) (* b b))
484.0ms
(exp (+ (* b b) (* (* c -4) a)))
411.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c -4) a) (* (* c -4) a))))
370.0ms
(- (* (* b b) (* b b)) (* (* (* c -4) a) (* (* c -4) a)))
291.0ms
(* (* (- (sqrt (+ (* b b) (* (* c -4) a))) b) (- (sqrt (+ (* b b) (* (* c -4) a))) b)) (- (sqrt (+ (* b b) (* (* c -4) a))) b))

prune866.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize49.0ms

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)))

rewrite113.0ms

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
54.0ms
(/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))
33.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
12.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
11.0ms
(+ (* b b) (* (* c -4) a))

series474.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
189.0ms
(/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))
127.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
88.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
70.0ms
(+ (* b b) (* (* c -4) a))

simplify24.9s

Counts
177 → 133
Calls
177 calls:
Slowest
1.2s
(* (* (/ 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))))
864.0ms
(- (* (sqrt (+ (* b b) (* (* c -4) a))) (sqrt (+ (* b b) (* (* c -4) a)))) (* b b))
781.0ms
(/ (* (* 1 1) 1) (/ (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* (- (sqrt (+ (* b b) (* (* c -4) a))) b) (- (sqrt (+ (* b b) (* (* c -4) a))) b)) (- (sqrt (+ (* b b) (* (* c -4) a))) b))))
560.0ms
(exp (+ (* b b) (* (* c -4) a)))
463.0ms
(- (* (* b b) (* b b)) (* (* (* c -4) a) (* (* c -4) a)))

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

localize31.0ms

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))

rewrite202.0ms

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
129.0ms
(* (/ 1/2 a) (- (sqrt (+ (* b b) (* (* a c) -4))) b))
50.0ms
(- (sqrt (+ (* b b) (* (* a c) -4))) b)
13.0ms
(sqrt (+ (* b b) (* (* a c) -4)))
8.0ms
(+ (* b b) (* (* a c) -4))

series485.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
210.0ms
(* (/ 1/2 a) (- (sqrt (+ (* b b) (* (* a c) -4))) b))
102.0ms
(- (sqrt (+ (* b b) (* (* a c) -4))) b)
101.0ms
(sqrt (+ (* b b) (* (* a c) -4)))
71.0ms
(+ (* b b) (* (* a c) -4))

simplify13.6s

Counts
115 → 100
Calls
115 calls:
Slowest
755.0ms
(- (* (sqrt (+ (* b b) (* (* a c) -4))) (sqrt (+ (* b b) (* (* a c) -4)))) (* b b))
627.0ms
(exp (+ (* b b) (* (* a c) -4)))
580.0ms
(sqrt (+ (pow (* b b) 3) (pow (* (* a c) -4) 3)))
567.0ms
(* 1/2 (- (* (sqrt (+ (* b b) (* (* a c) -4))) (sqrt (+ (* b b) (* (* a c) -4)))) (* b b)))
518.0ms
(+ (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

regimes299.0ms

Accuracy

87% (3.6b remaining)

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

bsearch786.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.6s1061×body2560valid
958.0ms5869×body80valid
630.0ms877×body1280valid
419.0ms2830×body80nan
298.0ms439×body640valid
96.0ms103×body5120valid
95.0ms239×body320valid
31.0ms116×body160valid