Details

Time bar (total: 1.4m)

sample515.0ms

Algorithm
intervals
Results
130.0ms52×body1280valid
125.0ms44×body640valid
78.0ms151×body80valid
26.0ms22×body320valid
16.0ms51×body80nan
6.0ms8×body160valid

simplify393.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
392.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize44.0ms

Local error

Found 4 expressions with local error:

19.0b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.7b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b
(/ x (tan B))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×add-exp-log
19×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube
12×times-frac
7×unpow-prod-down associate-*l*
6×associate-/r* prod-exp
5×pow1 div-exp
4×insert-posit16 associate-/l* add-log-exp
3×pow-to-exp cbrt-undiv pow-unpow associate-*r* pow-exp unswap-sqr sqr-pow
2×clear-num frac-2neg cbrt-unprod div-inv
1×pow-pow tan-quot associate-/r/ *-commutative
Counts
4 → 97
Calls
4 calls:
Slowest
132.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
45.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
19.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms
(/ x (tan B))

series580.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
145.0ms
(/ x (tan B))
117.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
111.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify10.0s

Counts
79 → 109
Calls
79 calls:
Slowest
554.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
534.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
527.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
475.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
472.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

18.9b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
18.9b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
0.7b
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
0.6b
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
51×add-exp-log
50×add-sqr-sqrt
44×unpow-prod-down
28×prod-exp sqrt-prod
20×*-un-lft-identity add-cube-cbrt
16×unswap-sqr
15×add-cbrt-cube
12×pow-to-exp swap-sqr pow-exp sqr-pow
11×div-exp
10×associate-*r* associate-*l*
6×pow1
4×sqrt-div cbrt-unprod insert-posit16 add-log-exp
3×cbrt-undiv associate-/r* times-frac
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×pow2 clear-num frac-2neg pow-prod-down pow-sqr *-commutative pow-prod-up div-inv associate-/l*
Counts
4 → 135
Calls
4 calls:
Slowest
194.0ms
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
150.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
14.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
13.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

series446.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
212.0ms
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
88.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
79.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
66.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

simplify29.0s

Counts
140 → 147
Calls
140 calls:
Slowest
733.0ms
(/ (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (sqrt (sin B)))
657.0ms
(/ (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) 1)
616.0ms
(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F)) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F)) (* (* (sin B) (sin B)) (sin B)))
552.0ms
(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (* F F) F)) (* (* (sin B) (sin B)) (sin B)))
516.0ms
(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (* F F) F)) (* (* (sin B) (sin B)) (sin B)))

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize108.0ms

Local error

Found 4 expressions with local error:

19.9b
(cbrt (+ (+ 2 (* F F)) (* 2 x)))
19.9b
(cbrt (+ (+ 2 (* F F)) (* 2 x)))
19.9b
(cbrt (+ (+ 2 (* F F)) (* 2 x)))
18.9b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
Slowest
23.0ms
(cbrt (+ (+ 2 (* F F)) (* 2 x)))
22.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
8.0ms
(cbrt (+ (+ 2 (* F F)) (* 2 x)))
8.0ms
(cbrt (+ (+ 2 (* F F)) (* 2 x)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(cbrt (+ (+ 2 (* F F)) (* 2 x)))
135.0ms
(cbrt (+ (+ 2 (* F F)) (* 2 x)))
130.0ms
(cbrt (+ (+ 2 (* F F)) (* 2 x)))
91.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

simplify5.3s

Counts
34 → 70
Calls
34 calls:
Slowest
315.0ms
(cbrt (- (* (+ 2 (* F F)) (+ 2 (* F F))) (* (* 2 x) (* 2 x))))
303.0ms
(cbrt (- (* (+ 2 (* F F)) (+ 2 (* F F))) (* (* 2 x) (* 2 x))))
293.0ms
(cbrt (+ (pow (+ 2 (* F F)) 3) (pow (* 2 x) 3)))
277.0ms
(+ (pow (/ 1 F) -2/3) (* 2/3 (pow (/ 1 (pow F 4)) 1/3)))
277.0ms
(sqrt (+ (pow (+ 2 (* F F)) 3) (pow (* 2 x) 3)))

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize431.0ms

Local error

Found 4 expressions with local error:

18.9b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
18.9b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
18.9b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
0.7b
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2)) F) (sin B))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
53×add-exp-log
28×prod-exp
14×div-exp
13×add-cbrt-cube
12×add-sqr-sqrt
10×pow-exp
9×*-un-lft-identity add-cube-cbrt sqrt-prod
7×pow-to-exp pow1
6×sqrt-div
4×insert-posit16 add-log-exp
3×cbrt-undiv rem-sqrt-square associate-/r* sqrt-pow1 flip3-+ times-frac pow1/2 cbrt-unprod flip-+
1×clear-num frac-2neg div-inv associate-/l*
Counts
4 → 83
Calls
4 calls:
Slowest
148.0ms
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2)) F) (sin B))
28.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
16.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
13.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2)) F) (sin B))
78.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
75.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
70.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

simplify10.4s

Counts
60 → 95
Calls
60 calls:
Slowest
661.0ms
(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (* (* (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2)) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2))) (* (* F F) F)) (* (* (sin B) (sin B)) (sin B)))
603.0ms
(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2)) F) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2)) F)) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2)) F)) (* (* (sin B) (sin B)) (sin B)))
523.0ms
(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2)) (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2))) (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2))) (* (* F F) F)) (* (* (sin B) (sin B)) (sin B)))
485.0ms
(/ (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2)) (sqrt (sin B)))
388.0ms
(- (+ (+ (* (log (sqrt (+ (+ 2 (* F F)) (* 2 x)))) -1/2) (* (log (* (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))))) -1/2)) (log F)) (log (sin B)))

prune1.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes450.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.6b

bsearch561.0ms

end0.0ms

sample13.6s

Algorithm
intervals
Results
5.9s1686×body1280valid
2.7s1351×body640valid
2.2s4853×body80valid
1.0s677×body320valid
732.0ms1658×body80nan
698.0ms311×body160valid