Details

analyze1.8s

Algorithm: search

sample65.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
18.0ms	147×	body	80	nan

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	17
1	106	17
2	374	17
3	1652	17
4	5001	17

prune6.0ms

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: 4.5b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.5b	(/ 2.0 (* t 3.0))
3.1b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.4b	(/ (* z (sqrt (+ t a))) t)

rewrite52.0ms

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` `associate--r+` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/r` `associate-/l`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `associate-*l/` `associate--l+` `clear-num` `div-inv` `associate-/l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

12.0ms	(* z (sqrt (+ t a)))
8.0ms	(/ 2.0 (* t 3.0))
22.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
7.0ms	(/ (* z (sqrt (+ t a))) t)

series80.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* z (sqrt (+ t a)))
4.0ms	(/ 2.0 (* t 3.0))
47.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
16.0ms	(/ (* z (sqrt (+ t a))) t)

simplify37.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1012	1260
1	5001	1212

prune219.0ms

Filtered

88 candidates to 113 candidates (-28.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Merged error: 0.3b

Counts

114 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
1.6b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
3.1b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`frac-sub`
58×	`times-frac`
47×	`*-un-lft-identity`
46×	`associate-r`
39×	`frac-times`
35×	`add-cube-cbrt`
31×	`cbrt-prod`
28×	`sqrt-prod`
27×	`associate-*r/`
25×	`add-exp-log` `flip3--` `flip--`
21×	`associate-*l/`
18×	`add-cbrt-cube`
10×	`unswap-sqr`
9×	`flip3-+` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`pow1` `distribute-lft-out` `associate--r+` `add-log-exp`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`pow1/3` `associate--l+` `div-inv`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 169

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
21.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
18.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

series119.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt t)
22.0ms	(cbrt t)
20.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
57.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1754	3649
1	5002	3540

prune401.0ms

Filtered

145 candidates to 181 candidates (-24.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	181	2	183

Merged error: 0.3b

Counts

183 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

3.3b	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
3.6b	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
7.7b	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
30.5b	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

766×	`associate-*l/`
764×	`associate-*r/`
524×	`frac-sub`
498×	`flip3--` `flip--`
364×	`frac-times`
240×	`sqrt-div`
162×	`associate-/l/`
120×	`flip3-+` `flip-+`
28×	`add-exp-log` `add-cbrt-cube`
16×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
12×	`prod-exp` `cbrt-unprod`
9×	`sub-neg`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `associate--r+`
7×	`associate-l`
6×	`pow-prod-down` `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` `difference-of-squares`

Counts

4 → 437

Calls

4 calls:

7.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
17.0ms	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
37.0ms	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
54.0ms	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
46.0ms	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
175.0ms	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
248.0ms	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify316.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (91.0ms)

Iter	Nodes	Cost
0	4640	24427
1	5001	24209

prune10.8s

Filtered

410 candidates to 449 candidates (-9.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	449	2	451

Merged error: 0.0b

Counts

451 → 2

localize38.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (* t (- b c)) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))
3.3b	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
7.7b	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* t (- b c)) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
30.5b	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* t (- b c)) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

766×	`associate-*l/`
662×	`associate-*r/`
524×	`frac-sub`
498×	`flip3--` `flip--`
364×	`frac-times`
240×	`sqrt-div`
162×	`associate-/l/`
120×	`flip3-+` `flip-+`
28×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-prod-down` `add-log-exp`
5×	`sub-neg` `associate-l`
4×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-r` `associate--r+`
3×	`times-frac` `associate-/l*`
2×	`associate-/r/` `*-commutative`
1×	`frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv` `difference-of-squares`

Counts

4 → 429

Calls

4 calls:

16.0ms	(* (* t (- b c)) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))
7.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
30.0ms	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* t (- b c)) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
56.0ms	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* t (- b c)) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* t (- b c)) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))
7.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
170.0ms	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* t (- b c)) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
252.0ms	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* t (- b c)) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify315.0ms

Algorithm

egg-herbie

Counts

441 → 441

Iterations

Useful iterations: 1 (94.0ms)

Iter	Nodes	Cost
0	4630	24558
1	5002	24339

prune10.1s

Filtered

408 candidates to 441 candidates (-8.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	441	0	441
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	441	2	443

Merged error: 0.0b

Counts

443 → 2

regimes612.0ms

Accuracy

-9.5% (2.3b remaining)

Error of 3.2b against oracle of 0.9b and baseline of 3.0b

bsearch4.7s

Steps

Iters	Range		Point
7	3.776935239243152e-282	1.8079331686906478e-280	5.077761223696634e-281
7	-7394757967451.191	-288863730592.96313	-293835684773.2317

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	56
1	79	56

end0.0ms

analyze1.8s

Algorithm: search

sample1.8s

Algorithm

intervals

Results

811.0ms	8000×	body	80	valid
483.0ms	4974×	body	80	nan

Details

analyze1.8s

sample65.0ms

simplify36.0ms

prune6.0ms

localize22.0ms

rewrite52.0ms

series80.0ms

simplify37.0ms

prune219.0ms

localize30.0ms

rewrite50.0ms

series119.0ms

simplify65.0ms

prune401.0ms

localize32.0ms

rewrite190.0ms

series476.0ms

simplify316.0ms

prune10.8s

localize38.0ms

rewrite179.0ms

series478.0ms

simplify315.0ms

prune10.1s

regimes612.0ms

bsearch4.7s

simplify2.0ms

end0.0ms

analyze1.8s

sample1.8s

Profiling