Details

sample73.0ms

Algorithm

intervals

Results

21.0ms	412×	body	80	nan
20.0ms	373×	body	80	valid

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (121.0ms)

Iter	Nodes	Cost
0	20	24
1	40	23
2	92	23
3	263	23
4	576	22
5	1144	22
6	2010	22
7	4222	22
done	5000	22

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.1b	(- (* (- x 0.5) (log x)) x)
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`associate-+l+` `add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*l/` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `fma-neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

25.0ms	(* (- x 0.5) (log x))
20.0ms	(- (* (- x 0.5) (log x)) x)
74.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
55.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

257.0ms	(* (- x 0.5) (log x))
408.0ms	(- (* (- x 0.5) (log x)) x)
415.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
89.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.0s

Counts

128 → 128

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	238	1852
1	574	1682
2	1607	1549
done	5000	1485

prune496.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
59.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series644.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt x)
179.0ms	(cbrt x)
191.0ms	(cbrt x)
91.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify966.0ms

Counts

82 → 82

Iterations

Useful iterations: 3 (363.0ms)

Iter	Nodes	Cost
0	101	939
1	225	870
2	630	794
3	1990	767
done	5000	767

prune430.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.5b	(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
5.0ms	(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

series682.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt x)
187.0ms	(cbrt x)
191.0ms	(cbrt x)
119.0ms	(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

simplify995.0ms

Counts

80 → 80

Iterations

Useful iterations: done (993.0ms)

Iter	Nodes	Cost
0	106	874
1	206	850
2	522	778
3	1470	757
done	5000	750

prune432.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (- x 0.5) (log x) (- 0.91893853320467 x))
0.3b	(fma (- x 0.5) (log x) (- 0.91893853320467 x))
0.5b	(* (sqrt (fma (- x 0.5) (log x) (- 0.91893853320467 x))) (sqrt (fma (- x 0.5) (log x) (- 0.91893853320467 x))))
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1`
18×	`sqrt-prod`
9×	`times-frac`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `swap-sqr` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `pow-sqr` `associate-/l`
2×	`fma-udef` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma (- x 0.5) (log x) (- 0.91893853320467 x))
0.0ms	(fma (- x 0.5) (log x) (- 0.91893853320467 x))
13.0ms	(* (sqrt (fma (- x 0.5) (log x) (- 0.91893853320467 x))) (sqrt (fma (- x 0.5) (log x) (- 0.91893853320467 x))))
57.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series956.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(fma (- x 0.5) (log x) (- 0.91893853320467 x))
292.0ms	(fma (- x 0.5) (log x) (- 0.91893853320467 x))
284.0ms	(* (sqrt (fma (- x 0.5) (log x) (- 0.91893853320467 x))) (sqrt (fma (- x 0.5) (log x) (- 0.91893853320467 x))))
92.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.8s

Counts

114 → 114

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	164	2438
1	353	1815
2	966	1626
3	3139	1536
done	5002	1491

prune388.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.4b

regimes602.0ms

Accuracy

80% (0.8b remaining)

Error of 2.8b against oracle of 2.0b and baseline of 6.0b

bsearch122.0ms

Steps

Iters	Range		Point
6	1.4167956326228866e+140	6.121681013265194e+140	5.427653638664575e+140
6	254195247935743.44	2396706146367806.5	520673369551077.94

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	104
1	76	104
done	76	104

end0.0ms

sample1.9s

Algorithm

intervals

Results

615.0ms	11597×	body	80	valid
529.0ms	11507×	body	80	nan