Details

Time bar (total: 12.9s)

sample49.0ms

Algorithm
intervals
Results
21.0ms283×body80valid
4.0ms107×body80nan

simplify81.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.0b
(* (* x y) z)
10.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.2b
(sqrt (- (* z z) (* t a)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
15.0ms
(- (* z z) (* t a))
25.0ms
(* (* x y) z)
55.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
19.0ms
(sqrt (- (* z z) (* t a)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* z z) (* t a))
29.0ms
(* (* x y) z)
125.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
84.0ms
(sqrt (- (* z z) (* t a)))

simplify943.0ms

Counts
88 → 88

prune387.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.0b
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
27.2b
(sqrt (- (* z z) (* t a)))
27.2b
(sqrt (- (* z z) (* t a)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
48×add-sqr-sqrt times-frac
35×add-cube-cbrt *-un-lft-identity
33×associate-*r*
30×add-exp-log add-cbrt-cube
16×sqrt-div
15×associate-*l*
9×cbrt-undiv div-exp prod-exp associate-/r* cbrt-unprod
8×pow1
6×associate-/r/
5×flip3-- flip--
4×add-log-exp unswap-sqr
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 141
Calls
4 calls:
26.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
124.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
18.0ms
(sqrt (- (* z z) (* t a)))
11.0ms
(sqrt (- (* z z) (* t a)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
130.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
94.0ms
(sqrt (- (* z z) (* t a)))
91.0ms
(sqrt (- (* z z) (* t a)))

simplify1.2s

Counts
153 → 153

prune767.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.5b

localize35.0ms

Local error

Found 4 expressions with local error:

5.4b
(/ (* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) z) (sqrt (sqrt (- (* z z) (* t a)))))
6.7b
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) z)
27.2b
(sqrt (- (* z z) (* t a)))
27.2b
(sqrt (- (* z z) (* t a)))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
33×sqrt-prod
27×add-exp-log add-cbrt-cube
21×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt *-un-lft-identity
15×associate-*l*
12×sqrt-div
9×associate-/r*
8×pow1 cbrt-undiv div-exp prod-exp cbrt-unprod
4×flip3-- associate-/r/ flip-- add-log-exp
3×associate-*r*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ div-inv
1×frac-2neg pow-prod-down clear-num *-commutative associate-/l/ associate-/l* unswap-sqr
Counts
4 → 105
Calls
4 calls:
73.0ms
(/ (* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) z) (sqrt (sqrt (- (* z z) (* t a)))))
81.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) z)
16.0ms
(sqrt (- (* z z) (* t a)))
13.0ms
(sqrt (- (* z z) (* t a)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) z) (sqrt (sqrt (- (* z z) (* t a)))))
169.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) z)
106.0ms
(sqrt (- (* z z) (* t a)))
79.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
117 → 117

prune471.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.5b

localize31.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (/ x 1) (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
4.7b
(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
27.2b
(sqrt (- (* z z) (* t a)))
27.2b
(sqrt (- (* z z) (* t a)))

rewrite361.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
87×times-frac
84×sqrt-prod
75×add-exp-log
57×add-cbrt-cube
51×add-cube-cbrt *-un-lft-identity
46×associate-*l*
34×associate-*r*
31×prod-exp
26×div-exp
22×cbrt-unprod
17×cbrt-undiv
16×unswap-sqr
13×pow1
12×sqrt-div
6×frac-times associate-*r/
5×1-exp
4×flip3-- pow-prod-down associate-*l/ associate-/r/ flip-- add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
Counts
4 → 188
Calls
4 calls:
161.0ms
(* (/ x 1) (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
171.0ms
(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
10.0ms
(sqrt (- (* z z) (* t a)))
9.0ms
(sqrt (- (* z z) (* t a)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (/ x 1) (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
67.0ms
(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
80.0ms
(sqrt (- (* z z) (* t a)))
77.0ms
(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts
200 → 200

prune834.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 3.5b

regimes496.0ms

Accuracy

80.6% (4.1b remaining)

Error of 7.8b against oracle of 3.8b and baseline of 24.7b

bsearch147.0ms

Steps
ItersRangePoint
9
2.8991777347275814e+54
1.8824221155203603e+62
1.4778266281396745e+58
8
-9.053793044056362e+41
-4.203803374477343e+37
-4.404844999539599e+41

simplify760.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
625.0ms8856×body80valid
235.0ms2914×body80nan