Details

sample87.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
26.0ms	279×	body	80	nan

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	17
1	108	17
2	389	17
3	1761	17
4	5002	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: 5.5b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.4b	(/ 2.0 (* t 3.0))
3.5b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
7.2b	(/ (* z (sqrt (+ t a))) t)

rewrite53.0ms

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:

7.0ms	(* z (sqrt (+ t a)))
5.0ms	(/ 2.0 (* t 3.0))
24.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
8.0ms	(/ (* z (sqrt (+ t a))) t)

series339.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* z (sqrt (+ t a)))
16.0ms	(/ 2.0 (* t 3.0))
178.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
80.0ms	(/ (* z (sqrt (+ t a))) t)

simplify55.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1377	2637
1	5001	2324

prune830.0ms

Filtered

191 candidates to 137 candidates (71.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	188	3	191
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	3	192

Merged error: 0.5b

Counts

192 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
2.8b	(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series867.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt t)
181.0ms	(cbrt t)
175.0ms	(cbrt t)
333.0ms	(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	144	371
1	345	322
2	1221	312
3	5001	306

prune342.0ms

Filtered

61 candidates to 54 candidates (88.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	61	3	64

Merged error: 0.5b

Counts

64 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x (* y (exp (* 2.0 (fma c 0.8333333333333334 (* a (- c b))))))))
0.0b	(* a (- c b))
0.0b	(fma c 0.8333333333333334 (* a (- c b)))
0.0b	(exp (* 2.0 (fma c 0.8333333333333334 (* a (- c b)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`prod-diff`
12×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `associate-/r` `fma-udef` `associate-/l`
2×	`sub-neg` `associate-*r/` `exp-sum` `associate-/r/`
1×	`cbrt-undiv` `exp-prod` `flip3--` `exp-to-pow` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `div-inv` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

4.0ms	(/ x (+ x (* y (exp (* 2.0 (fma c 0.8333333333333334 (* a (- c b))))))))
7.0ms	(* a (- c b))
1.0ms	(fma c 0.8333333333333334 (* a (- c b)))
2.0ms	(exp (* 2.0 (fma c 0.8333333333333334 (* a (- c b)))))

series200.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ x (+ x (* y (exp (* 2.0 (fma c 0.8333333333333334 (* a (- c b))))))))
33.0ms	(* a (- c b))
40.0ms	(fma c 0.8333333333333334 (* a (- c b)))
30.0ms	(exp (* 2.0 (fma c 0.8333333333333334 (* a (- c b)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	397	940
1	1506	743
2	5002	730

prune257.0ms

Filtered

113 candidates to 70 candidates (61.9%)

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: 0.5b

Counts

116 → 3

localize33.0ms

Local error

Found 4 expressions with local error:

4.6b	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
5.6b	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
8.0b	(- (* (* 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)))))
27.7b	(/ (- (* (* 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))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite203.0ms

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:

18.0ms	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
8.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
40.0ms	(- (* (* 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:

177.0ms	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
46.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
593.0ms	(- (* (* 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)))))
679.0ms	(/ (- (* (* 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))))

simplify317.0ms

Algorithm

egg-herbie

Counts

467 → 467

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4906	23936
1	5001	23936

prune5.8s

Filtered

467 candidates to 433 candidates (92.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	466	1	467
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	467	3	470

Merged error: 0b

Counts

470 → 3

regimes265.0ms

Accuracy

-11.6% (2.0b remaining)

Error of 2.0b against oracle of 0.1b and baseline of 1.8b

bsearch303.0ms

Steps

Iters	Range		Point
9	4.4615146373428735e+293	1.0576990443864383e+300	6.598436784322806e+296
7	3.719125391660263e+270	6.2770566847210874e+271	6.222952012630705e+271

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	42
1	73	42
2	73	42

end0.0ms

sample2.2s

Algorithm

intervals

Results

778.0ms	8000×	body	80	valid
737.0ms	7956×	body	80	nan