Details

sample86.0ms

Algorithm

intervals

Results

28.0ms	407×	body	80	nan
26.0ms	381×	body	80	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5251	24

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.4b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (- x 0.5) (log x)) x)
0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(* (- x 0.5) (log x))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `associate-+l+` `add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`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` `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 → 98

Calls

4 calls:

6.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(* (- x 0.5) (log x))
10.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series114.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* (- x 0.5) (log x)) x)
37.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
21.0ms	(* (- x 0.5) (log x))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify54.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5013	1429

prune213.0ms

Filtered

88 candidates to 110 candidates (-25.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	9	110
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	10	112

Merged error: 0.0b

Counts

112 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
0.1b	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
0.2b	(* (- x 0.5) (log x))
5.0b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

8.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
20.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
7.0ms	(* (- x 0.5) (log x))
11.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series77.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
31.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
23.0ms	(* (- x 0.5) (log x))
15.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5099	2246

prune213.0ms

Filtered

93 candidates to 119 candidates (-28.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Merged error: 0.0b

Counts

129 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.5b	(cbrt x)
0.5b	(cbrt x)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-prod` `associate-+l+`
12×	`associate-+r+`
9×	`times-frac`
8×	`associate-*l/`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3--` `frac-add` `flip--`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

13.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series174.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
21.0ms	(cbrt x)
26.0ms	(cbrt x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify66.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4948	1461
1	4948	1461

prune240.0ms

Filtered

99 candidates to 115 candidates (-16.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Merged error: 0.0b

Counts

124 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt x))
0.5b	(cbrt (sqrt x))
0.5b	(cbrt x)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`cbrt-prod`
9×	`times-frac`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`pow1` `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 → 68

Calls

4 calls:

2.0ms	(cbrt (sqrt x))
2.0ms	(cbrt (sqrt x))
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series78.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(cbrt (sqrt x))
16.0ms	(cbrt (sqrt x))
22.0ms	(cbrt x)
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify30.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4955	873
1	4955	873

prune127.0ms

Filtered

62 candidates to 80 candidates (-29.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 0.0b

Counts

90 → 10

regimes614.0ms

Accuracy

94.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 6.1b

bsearch133.0ms

Steps

Iters	Range		Point
8	141895583052.57874	2226530799111926.8	145638950479.37927
9	-22353923108931756.0	-22033768.18136611	-306537321.28306544

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	102
1	71	102

end0.0ms

sample2.4s

Algorithm

intervals

Results

840.0ms	11701×	body	80	valid
746.0ms	11764×	body	80	nan

Details

sample86.0ms

simplify74.0ms

prune11.0ms

localize16.0ms

rewrite38.0ms

series114.0ms

simplify54.0ms

prune213.0ms

localize17.0ms

rewrite48.0ms

series77.0ms

simplify63.0ms

prune213.0ms

localize24.0ms

rewrite30.0ms

series174.0ms

simplify66.0ms

prune240.0ms

localize29.0ms

rewrite17.0ms

series78.0ms

simplify30.0ms

prune127.0ms

regimes614.0ms

bsearch133.0ms

simplify1.0ms

end0.0ms

sample2.4s

Profiling