Details

analyze451.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

sample36.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
3.0ms	38×	body	80	invalid
2.0ms	29×	body	80	nan

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	5577	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: 5.3b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

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

series89.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
37.0ms	(- (* (- x 0.5) (log x)) x)
22.0ms	(* (- x 0.5) (log x))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5026	1375

prune211.0ms

Filtered

83 candidates to 107 candidates (-28.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	97	10	107
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 0.0b

Counts

109 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite16.0ms

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` `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 → 62

Calls

4 calls:

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

series87.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt x)
22.0ms	(cbrt x)
21.0ms	(cbrt x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4934	765
1	4934	765

prune148.0ms

Filtered

58 candidates to 74 candidates (-27.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	74	10	84

Merged error: 0.0b

Counts

84 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
0.3b	(/ 1 (/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333)))
4.8b	(/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
66×	`add-sqr-sqrt`
64×	`*-un-lft-identity`
62×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube`
12×	`log-prod`
11×	`associate-/r/`
8×	`pow1` `div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `div-inv` `associate-/l*` `add-log-exp`
5×	`flip3-+` `associate-l` `flip-+`
4×	`cbrt-undiv` `associate-r`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `flip--`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

7.0ms	(- (* (- x 0.5) (log x)) x)
7.0ms	(* (- x 0.5) (log x))
14.0ms	(/ 1 (/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333)))
11.0ms	(/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333))

series113.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* (- x 0.5) (log x)) x)
21.0ms	(* (- x 0.5) (log x))
22.0ms	(/ 1 (/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333)))
33.0ms	(/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333))

simplify76.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4968	3241
1	4968	3241

prune297.0ms

Filtered

120 candidates to 171 candidates (-42.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	170	11	181

Merged error: 0.0b

Counts

181 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (log x) (- x 0.5)))
0.5b	(cbrt (* (log x) (- x 0.5)))
0.5b	(* (cbrt (* (log x) (- x 0.5))) (cbrt (* (log x) (- x 0.5))))
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `associate-*r/`
16×	`add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`add-exp-log` `flip3--` `pow1/3` `flip--`
6×	`cbrt-prod` `add-cbrt-cube`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

5.0ms	(cbrt (* (log x) (- x 0.5)))
5.0ms	(cbrt (* (log x) (- x 0.5)))
6.0ms	(* (cbrt (* (log x) (- x 0.5))) (cbrt (* (log x) (- x 0.5))))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series156.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt (* (log x) (- x 0.5)))
23.0ms	(cbrt (* (log x) (- x 0.5)))
85.0ms	(* (cbrt (* (log x) (- x 0.5))) (cbrt (* (log x) (- x 0.5))))
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify36.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5047	3562

prune410.0ms

Filtered

83 candidates to 102 candidates (-22.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	102	11	113

Merged error: 0.0b

Counts

113 → 11

regimes632.0ms

Accuracy

86.9% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 5.8b

bsearch4.0ms

Steps

Iters	Range		Point
1	8.011068112443751e+97	8.516138649346436e+97	8.137335746669422e+97

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	122	74
1	122	74

end0.0ms

sample893.0ms

Algorithm

intervals

Results

561.0ms	8000×	body	80	valid
84.0ms	1197×	body	80	invalid
44.0ms	722×	body	80	nan

Details

analyze451.0ms

sample36.0ms

simplify103.0ms

prune11.0ms

localize16.0ms

rewrite37.0ms

series89.0ms

simplify55.0ms

prune211.0ms

localize26.0ms

rewrite16.0ms

series87.0ms

simplify55.0ms

prune148.0ms

localize19.0ms

rewrite47.0ms

series113.0ms

simplify76.0ms

prune297.0ms

localize20.0ms

rewrite30.0ms

series156.0ms

simplify36.0ms

prune410.0ms

regimes632.0ms

bsearch4.0ms

simplify2.0ms

end0.0ms

sample893.0ms

Profiling