Details

sample174.0ms

Algorithm

intervals

Results

59.0ms	58×	body	10240	exit
26.0ms	39×	body	1280	valid
20.0ms	50×	body	640	valid
11.0ms	120×	body	80	valid
8.0ms	30×	body	320	valid
5.0ms	91×	body	80	nan
4.0ms	12×	body	640	nan
3.0ms	17×	body	160	valid
3.0ms	2×	body	2560	valid
3.0ms	6×	body	1280	nan
1.0ms	4×	body	320	nan
0.0ms	2×	body	160	nan

simplify542.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	33	13
3	48	13
4	66	13
5	78	13
6	100	13
7	126	13
8	150	13
9	203	13
10	284	13
11	290	13
done	290	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.9b	(log (+ (- 1.0 y) (* y (exp z))))
2.5b	(+ (- 1.0 y) (* y (exp z)))

rewrite614.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate-+l+` `div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

24.0ms	(* y (exp z))
112.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
20.0ms	(log (+ (- 1.0 y) (* y (exp z))))
453.0ms	(+ (- 1.0 y) (* y (exp z)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* y (exp z))
276.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
106.0ms	(log (+ (- 1.0 y) (* y (exp z))))
56.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify2.7s

Counts

92 → 92

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	203	1436
1	451	1388
2	1247	1271
3	3833	1268
done	5002	1268

prune489.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* y (exp z)))
0.4b	(cbrt (* y (exp z)))
2.4b	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
11.6b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-cbrt-cube`
3×	`log-prod`
2×	`cbrt-prod` `log-div` `associate-+l+` `flip3-+` `pow1/3` `sum-log` `flip-+`
1×	`+-commutative` `associate-+l-` `sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 47

Calls

4 calls:

14.0ms	(cbrt (* y (exp z)))
14.0ms	(cbrt (* y (exp z)))
78.0ms	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
65.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (* y (exp z)))
122.0ms	(cbrt (* y (exp z)))
128.0ms	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
98.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

simplify2.2s

Counts

59 → 59

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	128	1360
1	305	1309
2	830	646
3	2758	636
done	5001	632

prune392.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow z 2))
0.0b	(- x (/ (+ (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))) (log 1.0)) t))
4.5b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.9b	(/ (+ (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))) (log 1.0)) t)

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`add-exp-log`
11×	`associate-r`
10×	`times-frac` `add-cbrt-cube`
6×	`pow1` `associate-l` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unpow2` `difference-of-squares` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `diff-log` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 93

Calls

4 calls:

25.0ms	(* 0.5 (pow z 2))
74.0ms	(- x (/ (+ (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))) (log 1.0)) t))
55.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
68.0ms	(/ (+ (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))) (log 1.0)) t)

series553.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* 0.5 (pow z 2))
164.0ms	(- x (/ (+ (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))) (log 1.0)) t))
156.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
193.0ms	(/ (+ (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))) (log 1.0)) t)

simplify1.4s

Counts

105 → 105

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	192	1963
1	461	1859
2	1380	1720
done	5001	1545

prune573.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
4.8b	(/ (* z y) t)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-cube-cbrt`
3×	`times-frac` `associate-/r*`
2×	`pow1` `cbrt-undiv` `diff-log` `div-exp`
1×	`sub-neg` `flip3--` `frac-2neg` `prod-exp` `clear-num` `sum-log` `flip--` `cbrt-unprod` `div-inv` `associate-/l*` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 37

Calls

2 calls:

87.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
13.0ms	(/ (* z y) t)

series151.0ms

Counts

2 → 6

Calls

2 calls:

116.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
35.0ms	(/ (* z y) t)

simplify2.4s

Counts

43 → 43

Iterations

Useful iterations: 2 (134.0ms)

Iter	Nodes	Cost
0	86	587
1	204	564
2	682	506
3	2974	506
done	5000	506

prune132.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.5b

regimes880.0ms

Accuracy

54.3% (6.2b remaining)

Error of 9.9b against oracle of 3.7b and baseline of 17.2b

bsearch3.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	51	143
1	63	143
done	63	143

end0.0ms

sample6.1s

Algorithm

intervals

Results

1.6s	1461×	body	10240	exit
1.2s	1386×	body	1280	valid
764.0ms	1593×	body	640	valid
620.0ms	2526×	body	80	nan
403.0ms	3570×	body	80	valid
357.0ms	910×	body	320	valid
132.0ms	79×	body	2560	valid
83.0ms	490×	body	160	valid
80.0ms	261×	body	640	nan
74.0ms	186×	body	320	nan
51.0ms	116×	body	1280	nan
13.0ms	104×	body	160	nan