Details

sample89.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
26.0ms	292×	body	80	nan

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	50	17
1	108	17
2	389	17
3	1761	17
4	5002	17

prune4.0ms

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: 4.0b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
2.4b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.2b	(/ (* z (sqrt (+ t a))) t)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
63×	`prod-diff`
62×	`associate--r+`
49×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
36×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
20×	`frac-sub`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-lft-out`
12×	`div-inv`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`fma-neg` `associate-r`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`sub-neg` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `associate-*l/` `associate--l+` `clear-num` `associate-/l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 179

Calls

4 calls:

11.0ms	(* z (sqrt (+ t a)))
5.0ms	(/ 2.0 (* t 3.0))
25.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
8.0ms	(/ (* z (sqrt (+ t a))) t)

series340.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* z (sqrt (+ t a)))
16.0ms	(/ 2.0 (* t 3.0))
179.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
83.0ms	(/ (* z (sqrt (+ t a))) t)

simplify55.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1377	2637
1	5001	2324

prune812.0ms

Filtered

191 candidates to 137 candidates (71.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	2	192

Merged error: 0.2b

Counts

192 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
0.3b	(/ (sqrt (+ t a)) t)
0.3b	(/ 2.0 (* t 3.0))
2.3b	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-un-lft-identity`
60×	`add-sqr-sqrt`
56×	`prod-diff`
54×	`add-cube-cbrt`
48×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
19×	`distribute-lft-out`
16×	`sqrt-prod`
13×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv` `associate-/l*`
8×	`frac-times` `flip3--` `flip--`
6×	`pow1` `associate-r` `frac-sub`
5×	`associate-l`
4×	`expm1-log1p-u` `flip3-+` `associate-r/` `associate-/r` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
2×	`sub-neg` `frac-2neg` `sqrt-div` `associate-*l/` `prod-exp` `associate--l+` `clear-num` `cbrt-unprod` `associate-/l/` `difference-of-squares`
1×	`pow-prod-down` `*-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 181

Calls

4 calls:

21.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
7.0ms	(/ (sqrt (+ t a)) t)
5.0ms	(/ 2.0 (* t 3.0))
1.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
58.0ms	(/ (sqrt (+ t a)) t)
16.0ms	(/ 2.0 (* t 3.0))
215.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify108.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	894	2691
1	4023	2163
2	5002	2158

prune641.0ms

Filtered

193 candidates to 108 candidates (56.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	192	3	195

Merged error: 0b

Counts

195 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.6666666666666666 (/ b t))
0.3b	(/ (sqrt (+ t a)) t)
2.4b	(fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))
2.5b	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
31×	`times-frac`
28×	`add-cube-cbrt`
16×	`sqrt-prod`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-l` `associate-/r*`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+`

Counts

4 → 101

Calls

4 calls:

7.0ms	(* 0.6666666666666666 (/ b t))
9.0ms	(/ (sqrt (+ t a)) t)
1.0ms	(fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))
1.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* 0.6666666666666666 (/ b t))
61.0ms	(/ (sqrt (+ t a)) t)
44.0ms	(fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))
220.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	419	756
1	1551	683
2	5001	673

prune454.0ms

Filtered

113 candidates to 81 candidates (71.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	113	3	116

Merged error: 0b

Counts

116 → 3

localize36.0ms

Local error

Found 4 expressions with local error:

3.5b	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
3.9b	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
5.7b	(- (* (* 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)))))
27.1b	(/ (- (* (* 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))))

rewrite212.0ms

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`
24×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
12×	`prod-exp` `cbrt-unprod` `associate--r+`
9×	`sub-neg` `prod-diff`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
6×	`pow-prod-down` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`times-frac` `associate-/l*`
2×	`associate-r` `associate-/r/` `*-commutative`
1×	`frac-2neg` `fma-neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv` `difference-of-squares`

Counts

4 → 455

Calls

4 calls:

8.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
20.0ms	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
42.0ms	(- (* (* 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)))))
59.0ms	(/ (- (* (* 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))))

series1.5s

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
179.0ms	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
587.0ms	(- (* (* 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)))))
699.0ms	(/ (- (* (* 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))))

simplify311.0ms

Algorithm

egg-herbie

Counts

467 → 467

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4906	23936
1	5001	23936

prune5.6s

Filtered

467 candidates to 433 candidates (92.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	467	0	467
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	467	3	470

Merged error: 0b

Counts

470 → 3

regimes256.0ms

Accuracy

0% (1.6b remaining)

Error of 2.1b against oracle of 0.5b and baseline of 2.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	18
1	45	18
2	45	18

end0.0ms

sample2.2s

Algorithm

intervals

Results

743.0ms	8247×	body	80	nan
741.0ms	8000×	body	80	valid