Details

Time bar (total: 9.6s)

sample95.0ms

Algorithm
intervals
Results
28.0ms335×body80nan
21.0ms325×body80valid

simplify1.1s

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
2.4b
(- (* y y) (* z z))
27.3b
(sqrt (- (* y y) (* z z)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
7×add-cube-cbrt *-un-lft-identity associate-*r*
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div
3×flip3-- associate-*l* flip-- difference-of-squares
2×associate-*r/ unswap-sqr
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
3 → 54
Calls
3 calls:
42.0ms
(* x (sqrt (- (* y y) (* z z))))
8.0ms
(- (* y y) (* z z))
10.0ms
(sqrt (- (* y y) (* z z)))

series225.0ms

Counts
3 → 9
Calls
3 calls:
119.0ms
(* x (sqrt (- (* y y) (* z z))))
55.0ms
(- (* y y) (* z z))
51.0ms
(sqrt (- (* y y) (* z z)))

simplify1.1s

Counts
63 → 63

prune163.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify11.0ms

Counts
0 → 0

prune4.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ y z))
0.0b
(sqrt (- y z))
0.3b
(* (sqrt (+ y z)) (sqrt (- y z)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
22×sqrt-prod
17×*-un-lft-identity
16×sqrt-div
9×pow1 add-cube-cbrt
8×associate-*r*
7×associate-*l*
5×add-exp-log add-cbrt-cube
4×frac-times flip3-- sqrt-pow1 flip3-+ pow1/2 flip-- flip-+ unswap-sqr
3×pow-prod-down add-log-exp
2×rem-sqrt-square associate-*r/ associate-*l/ distribute-lft-out distribute-lft-out-- difference-of-squares
1×sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
3 → 74
Calls
3 calls:
7.0ms
(sqrt (+ y z))
7.0ms
(sqrt (- y z))
47.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

series204.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(sqrt (+ y z))
69.0ms
(sqrt (- y z))
82.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

simplify864.0ms

Counts
83 → 83

prune295.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (fabs (cbrt (- y z))) (sqrt (+ y z))) (sqrt (cbrt (- y z))))
0.2b
(* (fabs (cbrt (- y z))) (sqrt (+ y z)))
0.5b
(cbrt (- y z))
0.5b
(cbrt (- y z))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
20×*-un-lft-identity
18×associate-*r*
15×cbrt-prod
14×sqrt-div
13×sqrt-prod
12×add-cube-cbrt
11×pow1 add-exp-log add-cbrt-cube
10×cbrt-div associate-*r/
5×flip3-- flip--
4×frac-times flip3-+ associate-*l* pow-prod-down prod-exp cbrt-unprod flip-+ add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1/3 associate-*l/ *-commutative unswap-sqr
1×distribute-lft-out
Counts
4 → 89
Calls
4 calls:
75.0ms
(* (* (fabs (cbrt (- y z))) (sqrt (+ y z))) (sqrt (cbrt (- y z))))
40.0ms
(* (fabs (cbrt (- y z))) (sqrt (+ y z)))
8.0ms
(cbrt (- y z))
8.0ms
(cbrt (- y z))

series665.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(* (* (fabs (cbrt (- y z))) (sqrt (+ y z))) (sqrt (cbrt (- y z))))
63.0ms
(* (fabs (cbrt (- y z))) (sqrt (+ y z)))
200.0ms
(cbrt (- y z))
198.0ms
(cbrt (- y z))

simplify1.0s

Counts
101 → 101

prune443.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes385.0ms

Accuracy

97.1% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 25.8b

bsearch246.0ms

Steps
ItersRangePoint
10
-2.872139137343122e-231
-2.5272618514179185e-248
-2.5767584462946616e-248

simplify29.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
962.0ms10176×body80valid
594.0ms10341×body80nan