Details

Time bar (total: 13.4s)

sample66.0ms

Algorithm
intervals
Results
18.0ms212×body80valid
11.0ms21×body2560valid
7.0ms256×pre80true
5.0ms12×body1280valid
2.0ms7×body640valid
1.0ms3×body320valid
1.0ms1×body5120valid

simplify69.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.1b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
16×sqrt-prod
8×pow1
6×add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp pow-prod-down clear-num sum-log div-inv distribute-lft-out
Counts
4 → 81
Calls
4 calls:
71.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
54.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
74.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
44.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series658.0ms

Counts
4 → 12
Calls
4 calls:
385.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
69.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
119.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
85.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.3s

Counts
93 → 93

prune444.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.8b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
10×pow1
9×add-cbrt-cube
6×sqrt-div add-log-exp
5×unswap-sqr
4×flip3-+ prod-exp flip-+
3×sqrt-pow1 associate-*r/ associate-*l*
2×pow1/2 div-exp pow-prod-down associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp 1-exp sum-log un-div-inv *-commutative div-inv
Counts
4 → 88
Calls
4 calls:
13.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
125.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series647.0ms

Counts
4 → 12
Calls
4 calls:
426.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
73.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
87.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify790.0ms

Counts
100 → 100

prune421.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.8b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
1.8b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
23×*-un-lft-identity
22×times-frac
21×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×add-log-exp
5×log-pow unswap-sqr
4×exp-prod sqrt-div prod-exp
3×log-prod flip3-+ associate-*l* flip-+
2×div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ rem-log-exp pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
4 → 91
Calls
4 calls:
127.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
11.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series681.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
420.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
95.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
75.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify872.0ms

Counts
103 → 103

prune895.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.5b

localize37.0ms

Local error

Found 4 expressions with local error:

1.3b
(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
1.8b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
1.8b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
11×log-prod log-pow
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×pow1 exp-prod
6×add-log-exp
5×add-exp-log sqrt-prod
4×add-cbrt-cube
2×flip3-+ sqrt-div rem-log-exp flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 59
Calls
4 calls:
2.0ms
(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
3.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
7.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
38.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series981.0ms

Counts
4 → 12
Calls
4 calls:
424.0ms
(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
380.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
98.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
78.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.2s

Counts
71 → 71

prune359.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

regimes292.0ms

Accuracy

79.1% (1.4b remaining)

Error of 8.7b against oracle of 7.3b and baseline of 14.1b

bsearch2.0ms

simplify507.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s6035×body80valid
375.0ms778×body2560valid
259.0ms619×body1280valid
203.0ms8000×pre80true
77.0ms281×body640valid
39.0ms74×body5120valid
29.0ms147×body320valid
8.0ms66×body160valid