Details

sample68.0ms

Algorithm

intervals

Results

19.0ms	250×	body	80	nan
17.0ms	256×	body	80	valid

simplify34.0ms

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

prune5.0ms

Filtered

1 candidates to 0 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: 3.5b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* t 3.0))
0.3b	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
1.9b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.4b	(/ (* z (sqrt (+ t a))) t)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

5.0ms	(/ 2.0 (* t 3.0))
16.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
12.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
7.0ms	(/ (* z (sqrt (+ t a))) t)

series319.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 2.0 (* t 3.0))
58.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
169.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
76.0ms	(/ (* z (sqrt (+ t a))) t)

simplify41.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1002	1658
1	5001	1593

prune653.0ms

Filtered

131 candidates to 101 candidates (77.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	3	132

Merged error: 0.2b

Counts

132 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
1.7b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
1.9b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

rewrite57.0ms

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

series693.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt t)
184.0ms	(cbrt t)
106.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
224.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

simplify76.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1739	3626
1	5001	3513

prune1.1s

Filtered

181 candidates to 144 candidates (79.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	181	3	184

Merged error: 0.2b

Counts

184 → 3

localize44.0ms

Local error

Found 4 expressions with local error:

4.9b	(* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0)))
4.9b	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
8.8b	(- (* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* (cbrt t) (cbrt t)) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
28.0b	(/ (- (* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* (cbrt t) (cbrt t)) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* (* (cbrt t) (cbrt t)) (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

469×	`associate-*l/`
467×	`associate-*r/`
320×	`frac-sub`
306×	`flip3--` `flip--`
202×	`frac-times`
102×	`associate-/l/`
74×	`add-exp-log`
65×	`add-cbrt-cube`
42×	`prod-exp` `cbrt-unprod`
30×	`pow1`
18×	`pow-prod-down`
10×	`cbrt-undiv` `div-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`sub-neg` `associate-l`
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 → 316

Calls

4 calls:

21.0ms	(* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0)))
8.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
230.0ms	(- (* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* (cbrt t) (cbrt t)) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
58.0ms	(/ (- (* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* (cbrt t) (cbrt t)) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* (* (cbrt t) (cbrt t)) (* (- a (/ 5.0 6.0)) (* t 3.0))))

series4.5s

Counts

4 → 12

Calls

4 calls:

255.0ms	(* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0)))
48.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
2.1s	(- (* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* (cbrt t) (cbrt t)) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
2.1s	(/ (- (* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* (cbrt t) (cbrt t)) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* (* (cbrt t) (cbrt t)) (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify234.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 1 (79.0ms)

Iter	Nodes	Cost
0	3751	16844
1	5001	16406

prune3.6s

Filtered

328 candidates to 276 candidates (84.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	327	1	328
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	328	3	331

Merged error: 0.2b

Counts

331 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b))))))
0.0b	(+ (* 1.0 (* a c)) (* 0.8333333333333334 c))
0.0b	(exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b)))))
0.9b	(- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-log-exp`
12×	`exp-sum`
9×	`associate-r`
8×	`add-sqr-sqrt`
6×	`pow1` `distribute-rgt-in` `add-cube-cbrt` `*-un-lft-identity` `distribute-lft-in` `add-cbrt-cube`
5×	`add-exp-log` `sub-neg` `associate--l+`
3×	`associate-l`
2×	`diff-log` `sum-log`
1×	`+-commutative` `exp-prod` `flip3--` `exp-to-pow` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `rem-exp-log` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

16.0ms	(* y (exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b))))))
5.0ms	(+ (* 1.0 (* a c)) (* 0.8333333333333334 c))
8.0ms	(exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b)))))
8.0ms	(- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* y (exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b))))))
42.0ms	(+ (* 1.0 (* a c)) (* 0.8333333333333334 c))
50.0ms	(exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b)))))
47.0ms	(- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b)))

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	296	758
1	1159	678
2	5002	669

prune218.0ms

Filtered

77 candidates to 51 candidates (66.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	76	4	80

Merged error: 0b

Counts

80 → 4

regimes277.0ms

Accuracy

1.1% (2.1b remaining)

Error of 2.6b against oracle of 0.5b and baseline of 2.6b

bsearch433.0ms

Steps

Iters	Range		Point
9	-4.206901956195951e-280	-3.4447260752443994e-286	-2.353822028203789e-282
10	-1.4137927064806989e-42	-6.302369982881644e-61	-4.306054221796757e-56

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	64
1	79	64

end0.0ms

sample1.7s

Algorithm

intervals

Results

571.0ms	8000×	body	80	valid
534.0ms	8019×	body	80	nan