Details

sample68.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
17.0ms	244×	body	80	nan

simplify51.0ms

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

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: 5.3b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2.0 (* t 3.0))
0.2b	(* z (sqrt (+ t a)))
3.9b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.3b	(/ (* z (sqrt (+ t a))) t)

rewrite52.0ms

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:

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

series350.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 2.0 (* t 3.0))
62.0ms	(* z (sqrt (+ t a)))
172.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
100.0ms	(/ (* z (sqrt (+ t a))) t)

simplify61.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1377	2637
1	5001	2324

prune805.0ms

Filtered

191 candidates to 137 candidates (71.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	4	192

Merged error: 1.0b

Counts

192 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
2.5b	(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite7.0ms

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)
2.0ms	(cbrt t)
2.0ms	(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))))))

series833.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt t)
167.0ms	(cbrt t)
171.0ms	(cbrt t)
325.0ms	(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (34.0ms)

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

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	61	4	65

Merged error: 1.0b

Counts

65 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
1.0b	(log1p (expm1 (/ 2.0 (* t 3.0))))
5.3b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log1p (expm1 (/ 2.0 (* t 3.0)))))))
6.3b	(/ (* z (sqrt (+ t a))) t)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

8.0ms	(* z (sqrt (+ t a)))
1.0ms	(log1p (expm1 (/ 2.0 (* t 3.0))))
23.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log1p (expm1 (/ 2.0 (* t 3.0)))))))
8.0ms	(/ (* z (sqrt (+ t a))) t)

series1.2s

Counts

4 → 12

Calls

4 calls:

59.0ms	(* z (sqrt (+ t a)))
702.0ms	(log1p (expm1 (/ 2.0 (* t 3.0))))
331.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log1p (expm1 (/ 2.0 (* t 3.0)))))))
85.0ms	(/ (* z (sqrt (+ t a))) t)

simplify120.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	980	1995
1	4653	1665
2	5001	1611

prune665.0ms

Filtered

141 candidates to 106 candidates (75.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	142	3	145

Merged error: 0b

Counts

145 → 3

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2.0 (* t 3.0))
0.2b	(* z (sqrt (+ t a)))
2.3b	(fma (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0)))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))
6.3b	(/ (* z (sqrt (+ t a))) t)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

5.0ms	(/ 2.0 (* t 3.0))
7.0ms	(* z (sqrt (+ t a)))
1.0ms	(fma (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0)))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))
8.0ms	(/ (* z (sqrt (+ t a))) t)

series341.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 2.0 (* t 3.0))
58.0ms	(* z (sqrt (+ t a)))
166.0ms	(fma (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0)))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))
96.0ms	(/ (* z (sqrt (+ t a))) t)

simplify59.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	527	609
1	2180	526
2	5002	516

prune462.0ms

Filtered

97 candidates to 75 candidates (77.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	97	3	100

Merged error: 0b

Counts

100 → 3

regimes285.0ms

Accuracy

-14.7% (2.1b remaining)

Error of 2.1b against oracle of 0.0b and baseline of 1.9b

bsearch318.0ms

Steps

Iters	Range		Point
7	1.0194911374297609e-286	1.6367437277993015e-285	1.0277137801434701e-286
9	-7.141888443372673e-245	-6.309453960374173e-254	-9.607961150420862e-254

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	98	84
1	100	84
2	100	84

end0.0ms

sample1.8s

Algorithm

intervals

Results

603.0ms	8000×	body	80	valid
566.0ms	7808×	body	80	nan