Details

analyze1.7s

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
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

sample64.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
14.0ms	158×	body	80	nan

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5545	33

prune18.0ms

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: 2.5b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
2.2b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
4.1b	(/ (* z (sqrt (+ t a))) t)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

7.0ms	(* z (sqrt (+ t a)))
6.0ms	(/ 2.0 (* t 3.0))
13.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
7.0ms	(/ (* z (sqrt (+ t a))) t)

series83.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* z (sqrt (+ t a)))
2.0ms	(/ 2.0 (* t 3.0))
49.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
17.0ms	(/ (* z (sqrt (+ t a))) t)

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4965	2272
1	4965	2272

prune227.0ms

Filtered

87 candidates to 110 candidates (-26.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	3	112

Merged error: 0.2b

Counts

112 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* t 3.0))
1.3b	(log (exp (- (* (/ z t) (sqrt (+ t a))) (* (- b c) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))))))))
2.2b	(- (* (/ z t) (sqrt (+ t a))) (* (- b c) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))))))
5.6b	(* (/ z t) (sqrt (+ t a)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

40×	`frac-sub`
38×	`frac-times`
36×	`sqrt-div`
33×	`flip3-+` `flip-+`
28×	`associate-*r/`
27×	`add-sqr-sqrt`
19×	`-un-lft-identity` `associate-l/`
17×	`add-cube-cbrt`
16×	`flip3--` `flip--`
14×	`add-exp-log` `times-frac` `add-cbrt-cube`
13×	`associate-l`
7×	`pow1` `associate-r`
6×	`sqrt-prod` `add-log-exp`
4×	`log-prod` `log-pow` `unswap-sqr`
3×	`cbrt-undiv` `exp-prod` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`sub-neg` `div-inv` `associate--r+`
1×	`distribute-rgt-in` `log-div` `frac-2neg` `distribute-lft-in` `exp-diff` `diff-log` `rem-log-exp` `exp-sum` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `distribute-lft-out`

Counts

4 → 133

Calls

4 calls:

5.0ms	(/ 2.0 (* t 3.0))
8.0ms	(log (exp (- (* (/ z t) (sqrt (+ t a))) (* (- b c) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))))))))
13.0ms	(- (* (/ z t) (sqrt (+ t a))) (* (- b c) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))))))
10.0ms	(* (/ z t) (sqrt (+ t a)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 2.0 (* t 3.0))
50.0ms	(log (exp (- (* (/ z t) (sqrt (+ t a))) (* (- b c) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))))))))
54.0ms	(- (* (/ z t) (sqrt (+ t a))) (* (- b c) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))))))
17.0ms	(* (/ z t) (sqrt (+ t a)))

simplify40.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5468	5166

prune402.0ms

Filtered

121 candidates to 145 candidates (-19.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	145	3	148

Merged error: 0.2b

Counts

148 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* t 3.0))
2.8b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
4.1b	(log (exp (/ 2.0 (* t 3.0))))
4.1b	(/ (* z (sqrt (+ t a))) t)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`log-pow` `frac-sub`
7×	`exp-prod` `flip3--` `flip--`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-/r` `associate-/l*` `associate--r+`
3×	`sub-neg` `log-prod` `div-inv`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-div` `associate-*l/` `prod-exp` `associate--l+` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`flip3-+` `diff-log` `rem-log-exp` `flip-+`

Counts

4 → 86

Calls

4 calls:

5.0ms	(/ 2.0 (* t 3.0))
12.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
4.0ms	(log (exp (/ 2.0 (* t 3.0))))
8.0ms	(/ (* z (sqrt (+ t a))) t)

series79.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 2.0 (* t 3.0))
57.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
2.0ms	(log (exp (/ 2.0 (* t 3.0))))
17.0ms	(/ (* z (sqrt (+ t a))) t)

simplify36.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5035	1665

prune196.0ms

Filtered

79 candidates to 98 candidates (-24.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	98	3	101

Merged error: 0.2b

Counts

101 → 3

localize35.0ms

Local error

Found 4 expressions with local error:

4.6b	(* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0)))))
6.6b	(* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0))))))
8.2b	(- (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))) (* 2.0 (- a (/ 5.0 6.0)))))))
25.6b	(/ (- (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))) (* 2.0 (- a (/ 5.0 6.0))))))) (* t (* t (* 3.0 (- a (/ 5.0 6.0))))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

1904×	`associate-*r/`
512×	`frac-sub`
479×	`flip3--` `flip--`
356×	`frac-times`
246×	`sqrt-div`
162×	`associate-/l/`
123×	`flip3-+` `flip-+`
114×	`associate-*l/`
104×	`distribute-rgt-in` `distribute-lft-in`
57×	`sub-neg`
37×	`add-exp-log` `add-cbrt-cube`
32×	`associate--l+`
23×	`pow1`
20×	`associate--r+`
19×	`prod-exp` `cbrt-unprod`
13×	`pow-prod-down`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`times-frac` `associate-/l*`
2×	`associate-r` `associate-/r/` `*-commutative`
1×	`frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 469

Calls

4 calls:

9.0ms	(* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0)))))
19.0ms	(* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0))))))
45.0ms	(- (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))) (* 2.0 (- a (/ 5.0 6.0)))))))
61.0ms	(/ (- (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))) (* 2.0 (- a (/ 5.0 6.0))))))) (* t (* t (* 3.0 (- a (/ 5.0 6.0))))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0)))))
23.0ms	(* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0))))))
177.0ms	(- (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))) (* 2.0 (- a (/ 5.0 6.0)))))))
498.0ms	(/ (- (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))) (* 2.0 (- a (/ 5.0 6.0))))))) (* t (* t (* 3.0 (- a (/ 5.0 6.0))))))

simplify223.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5244	42986

prune11.5s

Filtered

435 candidates to 481 candidates (-10.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	481	0	481
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	481	3	484

Merged error: 0.2b

Counts

484 → 3

regimes670.0ms

Accuracy

-29.8% (3.0b remaining)

Error of 4.0b against oracle of 1.0b and baseline of 3.3b

bsearch44.0ms

Steps

Iters	Range		Point
2	5.209691673201319e+215	5.8326072163728355e+215	5.287556116097758e+215
5	9.407265342339727e+170	2.682698069534376e+171	2.6391929217903797e+171

simplify24.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	986	111
1	986	111

end0.0ms

sample1.7s

Algorithm

intervals

Results

776.0ms	8000×	body	80	valid
467.0ms	4925×	body	80	nan

Details

analyze1.7s

sample64.0ms

simplify30.0ms

prune18.0ms

localize22.0ms

rewrite37.0ms

series83.0ms

simplify52.0ms

prune227.0ms

localize30.0ms

rewrite45.0ms

series124.0ms

simplify40.0ms

prune402.0ms

localize27.0ms

rewrite32.0ms

series79.0ms

simplify36.0ms

prune196.0ms

localize35.0ms

rewrite225.0ms

series710.0ms

simplify223.0ms

prune11.5s

regimes670.0ms

bsearch44.0ms

simplify24.0ms

end0.0ms

sample1.7s

Profiling