Details

Time bar (total: 17.8s)

sample43.0ms

Algorithm
intervals
Results
15.0ms284×body80valid
4.0ms96×body80nan

simplify96.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37214
49714
511214
done11214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
3.9b
(* (* x y) z)
8.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite93.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u
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 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
10.0ms
(- (* z z) (* t a))
25.0ms
(* (* x y) z)
36.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
18.0ms
(sqrt (- (* z z) (* t a)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (* z z) (* t a))
42.0ms
(* (* x y) z)
170.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
78.0ms
(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts
98 → 98
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01461331
13611220
215601062
done50011060

prune497.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.4b
(- (* z z) (* t a))
2.9b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
24.0ms
(/ (sqrt (- (* z z) (* t a))) z)
16.0ms
(- (* z z) (* t a))
29.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms
(sqrt (- (* z z) (* t a)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(/ (sqrt (- (* z z) (* t a))) z)
55.0ms
(- (* z z) (* t a))
177.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
101.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
154 → 154
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02222758
15222513
216932314
done50012309

prune706.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt z) (cbrt z))
1.6b
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (cbrt (- (* z z) (* t a)))) (cbrt z))))
23.8b
(cbrt (- (* z z) (* t a)))
23.8b
(cbrt (- (* z z) (* t a)))

rewrite360.0ms

Algorithm
rewrite-expression-head
Rules
429×times-frac
309×add-sqr-sqrt
198×add-cube-cbrt *-un-lft-identity
185×associate-*r*
172×cbrt-prod
120×sqrt-prod
60×add-exp-log
48×add-cbrt-cube
32×associate-*l*
28×unswap-sqr
27×cbrt-undiv div-exp
16×prod-exp cbrt-unprod
13×pow1
8×pow1/3 div-inv
6×swap-sqr
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×pow-prod-down
2×flip3-- associate-/r/ pow-sqr *-commutative pow-prod-up flip--
1×pow2 frac-times pow-plus associate-*r/ associate-*l/
Counts
4 → 339
Calls
4 calls:
21.0ms
(* (cbrt z) (cbrt z))
289.0ms
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (cbrt (- (* z z) (* t a)))) (cbrt z))))
11.0ms
(cbrt (- (* z z) (* t a)))
6.0ms
(cbrt (- (* z z) (* t a)))

series1.1s

Counts
4 → 12
Calls
4 calls:
329.0ms
(* (cbrt z) (cbrt z))
523.0ms
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (cbrt (- (* z z) (* t a)))) (cbrt z))))
124.0ms
(cbrt (- (* z z) (* t a)))
134.0ms
(cbrt (- (* z z) (* t a)))

simplify1.7s

Counts
351 → 351
Iterations

Useful iterations: done (1.7s)

IterNodesCost
066312025
1207611259
done50009651

prune2.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.4b

localize47.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (/ x (/ (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (cbrt (- (* z z) (* t a)))) (cbrt z))))
23.0b
(sqrt (- (* z z) (* t a)))
23.0b
(sqrt (- (* z z) (* t a)))
23.8b
(cbrt (- (* z z) (* t a)))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
429×times-frac
296×add-sqr-sqrt
191×add-cube-cbrt *-un-lft-identity
179×associate-*r*
153×cbrt-prod
126×sqrt-prod
58×add-exp-log
48×add-cbrt-cube
27×cbrt-undiv div-exp
26×associate-*l*
24×unswap-sqr
15×prod-exp cbrt-unprod
8×pow1 div-inv
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×flip3-- flip--
2×rem-sqrt-square cbrt-div sqrt-pow1 pow1/2 associate-/r/
1×frac-times pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 316
Calls
4 calls:
247.0ms
(* (/ x (/ (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (cbrt (- (* z z) (* t a)))) (cbrt z))))
11.0ms
(sqrt (- (* z z) (* t a)))
11.0ms
(sqrt (- (* z z) (* t a)))
9.0ms
(cbrt (- (* z z) (* t a)))

series868.0ms

Counts
4 → 12
Calls
4 calls:
517.0ms
(* (/ x (/ (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (cbrt (- (* z z) (* t a)))) (cbrt z))))
95.0ms
(sqrt (- (* z z) (* t a)))
107.0ms
(sqrt (- (* z z) (* t a)))
147.0ms
(cbrt (- (* z z) (* t a)))

simplify1.5s

Counts
328 → 328
Iterations

Useful iterations: done (1.4s)

IterNodesCost
065915364
1207414598
done500013297

prune2.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 2.4b

regimes401.0ms

Accuracy

88.3% (2.2b remaining)

Error of 5.3b against oracle of 3.1b and baseline of 21.8b

bsearch108.0ms

Steps
ItersRangePoint
4
1.5523497138925845e+121
2.2438624246711994e+121
2.130897152856616e+121
8
-4.4687952358618183e+136
-2.295024957636829e+132
-2.7186746230671153e+135

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02958
13658
23858
done3858

end0.0ms

sample1.5s

Algorithm
intervals
Results
610.0ms8851×body80valid
186.0ms2869×body80nan