Details

analyze1.3s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
5.8%	93.9%	0.3%	11
8.4%	91.3%	0.3%	12
9.7%	90%	0.3%	13
10.7%	89%	0.3%	14

sample29.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
1.0ms	14×	body	80	invalid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	46	17
1	46	17

prune16.0ms

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: 13.2b

Counts

2 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

3.5b	(* y (/ z t))
3.8b	(* y (/ b t))
12.8b	(/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* y (/ b t)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
32×	`times-frac`
28×	`add-cube-cbrt`
26×	`associate-r`
15×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l`
4×	`prod-exp` `associate-/r*` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
3×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l*` `add-log-exp`
2×	`flip3-+` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `flip-+` `associate-/l/`
1×	`frac-2neg` `clear-num`

Counts

3 → 99

Calls

3 calls:

10.0ms	(* y (/ z t))
6.0ms	(* y (/ b t))
8.0ms	(/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* y (/ b t)))))

series52.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* y (/ z t))
5.0ms	(* y (/ b t))
41.0ms	(/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* y (/ b t)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5152	1325

prune203.0ms

Filtered

76 candidates to 108 candidates (-42.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	96	12	108
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	13	110

Merged error: 12.5b

Counts

110 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt b)
2.0b	(* y (* (/ (cbrt b) (cbrt t)) (/ (cbrt b) (cbrt t))))
3.5b	(* y (/ z t))
12.8b	(/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* (* y (* (/ (cbrt b) (cbrt t)) (/ (cbrt b) (cbrt t)))) (/ (cbrt b) (cbrt t))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
29×	`add-exp-log` `add-sqr-sqrt`
23×	`add-cube-cbrt`
22×	`times-frac`
21×	`add-cbrt-cube`
14×	`associate-r`
11×	`pow1` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `associate-l`
5×	`associate-*r/`
4×	`pow-prod-down` `associate-/r*` `distribute-lft-out` `add-log-exp`
3×	`cbrt-prod` `associate-/l*` `unswap-sqr`
2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `div-inv` `associate-/l/`
1×	`frac-times` `frac-2neg` `pow1/3` `associate-*l/` `clear-num`

Counts

4 → 106

Calls

4 calls:

1.0ms	(cbrt b)
14.0ms	(* y (* (/ (cbrt b) (cbrt t)) (/ (cbrt b) (cbrt t))))
6.0ms	(* y (/ z t))
10.0ms	(/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* (* y (* (/ (cbrt b) (cbrt t)) (/ (cbrt b) (cbrt t)))) (/ (cbrt b) (cbrt t))))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt b)
26.0ms	(* y (* (/ (cbrt b) (cbrt t)) (/ (cbrt b) (cbrt t))))
5.0ms	(* y (/ z t))
41.0ms	(/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* (* y (* (/ (cbrt b) (cbrt t)) (/ (cbrt b) (cbrt t)))) (/ (cbrt b) (cbrt t))))))

simplify32.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5096	1676

prune191.0ms

Filtered

80 candidates to 118 candidates (-47.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	118	13	131

Merged error: 12.5b

Counts

131 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (+ a (+ 1.0 (* y (/ b t)))))
3.5b	(* y (/ z t))
3.8b	(* y (/ b t))
12.5b	(* (+ x (* y (/ z t))) (/ 1 (+ a (+ 1.0 (* y (/ b t))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
46×	`times-frac`
44×	`associate-r`
38×	`add-cube-cbrt`
27×	`add-exp-log`
21×	`add-cbrt-cube`
11×	`pow1`
9×	`associate-l`
8×	`prod-exp`
7×	`distribute-lft-out` `unswap-sqr`
6×	`div-exp` `cbrt-unprod`
4×	`cbrt-undiv` `flip3-+` `associate-/r*` `associate-/r/` `flip-+` `div-inv` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `-commutative` `associate-/l*`
2×	`frac-times` `rec-exp` `1-exp` `associate-*l/`
1×	`pow-flip` `frac-2neg` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 146

Calls

4 calls:

6.0ms	(/ 1 (+ a (+ 1.0 (* y (/ b t)))))
6.0ms	(* y (/ z t))
6.0ms	(* y (/ b t))
13.0ms	(* (+ x (* y (/ z t))) (/ 1 (+ a (+ 1.0 (* y (/ b t))))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (+ a (+ 1.0 (* y (/ b t)))))
5.0ms	(* y (/ z t))
5.0ms	(* y (/ b t))
43.0ms	(* (+ x (* y (/ z t))) (/ 1 (+ a (+ 1.0 (* y (/ b t))))))

simplify33.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5063	1908

prune197.0ms

Filtered

98 candidates to 158 candidates (-61.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	160	11	171

Merged error: 12.5b

Counts

171 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

12.8b	(/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* (* (cbrt (* y (/ b t))) (cbrt (* y (/ b t)))) (cbrt (* y (/ b t)))))))
20.1b	(cbrt (* y (/ b t)))
20.1b	(cbrt (* y (/ b t)))
20.1b	(cbrt (* y (/ b t)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `associate-/r*` `distribute-lft-out` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-r/` `associate-/l`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 65

Calls

4 calls:

8.0ms	(/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* (* (cbrt (* y (/ b t))) (cbrt (* y (/ b t)))) (cbrt (* y (/ b t)))))))
4.0ms	(cbrt (* y (/ b t)))
4.0ms	(cbrt (* y (/ b t)))
4.0ms	(cbrt (* y (/ b t)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* (* (cbrt (* y (/ b t))) (cbrt (* y (/ b t)))) (cbrt (* y (/ b t)))))))
22.0ms	(cbrt (* y (/ b t)))
21.0ms	(cbrt (* y (/ b t)))
20.0ms	(cbrt (* y (/ b t)))

simplify82.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4877	1144
1	4877	1144

prune80.0ms

Filtered

57 candidates to 77 candidates (-35.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	77	11	88

Merged error: 12.5b

Counts

88 → 11

regimes1.1s

Accuracy

62.3% (1.4b remaining)

Error of 13.3b against oracle of 11.9b and baseline of 15.7b

bsearch44.0ms

Steps

Iters	Range		Point
9	1.0358713984788157e+24	3.431622165060943e+29	1.958815587896096e+26
8	-2.666282045454706e+96	-1.181650958175104e+93	-1.77287718798098e+94

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	45
1	45	45

end0.0ms

sample729.0ms

Algorithm

intervals

Results

423.0ms	8000×	body	80	valid
17.0ms	290×	body	80	invalid

Details

analyze1.3s

sample29.0ms

simplify4.0ms

prune16.0ms

localize13.0ms

rewrite28.0ms

series52.0ms

simplify41.0ms

prune203.0ms

localize19.0ms

rewrite37.0ms

series97.0ms

simplify32.0ms

prune191.0ms

localize14.0ms

rewrite38.0ms

series69.0ms

simplify33.0ms

prune197.0ms

localize16.0ms

rewrite20.0ms

series108.0ms

simplify82.0ms

prune80.0ms

regimes1.1s

bsearch44.0ms

simplify1.0ms

end0.0ms

sample729.0ms

Profiling