Details

sample75.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
20.0ms	227×	body	80	nan

simplify38.0ms

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: 4.5b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 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)))))
5.0b	(/ (* 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:

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)

series332.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* z (sqrt (+ t a)))
18.0ms	(/ 2.0 (* t 3.0))
174.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
80.0ms	(/ (* z (sqrt (+ t a))) t)

simplify61.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1377	2637
1	5001	2324

prune817.0ms

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: 0.7b

Counts

192 → 4

localize29.0ms

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))
2.4b	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite40.0ms

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:

19.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
6.0ms	(/ (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))))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
59.0ms	(/ (sqrt (+ t a)) t)
21.0ms	(/ 2.0 (* t 3.0))
209.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify113.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (86.0ms)

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

prune656.0ms

Filtered

193 candidates to 107 candidates (55.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	193	4	197

Merged error: 0.5b

Counts

197 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
4.0b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log1p (expm1 (/ 2.0 (* t 3.0)))))))
5.0b	(/ (* z (sqrt (+ t a))) t)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
31×	`prod-diff`
30×	`associate--r+`
29×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-rgt-in` `distribute-lft-in`
12×	`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×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `sqrt-div` `div-exp` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
3×	`sub-neg` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `flip3-+` `associate-*l/` `associate--l+` `clear-num` `flip-+` `associate-/l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 141

Calls

4 calls:

10.0ms	(* z (sqrt (+ t a)))
5.0ms	(/ 2.0 (* t 3.0))
19.0ms	(- (/ (* 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)

series422.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* z (sqrt (+ t a)))
21.0ms	(/ 2.0 (* t 3.0))
263.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log1p (expm1 (/ 2.0 (* t 3.0)))))))
80.0ms	(/ (* z (sqrt (+ t a))) t)

simplify127.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	1028	2010
1	4924	1664
2	5001	1614

prune697.0ms

Filtered

153 candidates to 112 candidates (73.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	155	2	157

Merged error: 0b

Counts

157 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* t 3.0))
0.3b	(/ 2.0 (* t 3.0))
1.1b	(fma (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0)))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))
5.0b	(/ (* z (sqrt (+ t a))) t)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`
2×	`sqrt-div` `associate-*r/` `associate-/l/`
1×	`flip3-+` `flip-+` `fma-udef`

Counts

4 → 81

Calls

4 calls:

5.0ms	(/ 2.0 (* t 3.0))
8.0ms	(/ 2.0 (* t 3.0))
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)

series278.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 2.0 (* t 3.0))
20.0ms	(/ 2.0 (* t 3.0))
168.0ms	(fma (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0)))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))
74.0ms	(/ (* z (sqrt (+ t a))) t)

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	415	538
1	1639	457
2	5002	454

prune445.0ms

Filtered

93 candidates to 73 candidates (78.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	93	2	95

Merged error: 0b

Counts

95 → 2

regimes223.0ms

Accuracy

33.3% (1.3b remaining)

Error of 1.6b against oracle of 0.3b and baseline of 2.2b

bsearch154.0ms

Steps

Iters	Range		Point
8	4.094979821473785e-123	1.4379210740990664e-120	1.1163399401523421e-121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	46
1	71	46
2	71	46

end0.0ms

sample2.2s

Algorithm

intervals

Results

774.0ms	8000×	body	80	valid
745.0ms	7937×	body	80	nan