Details

sample98.0ms

Algorithm

intervals

Results

23.0ms	48×	body	1280	valid
21.0ms	42×	body	10240	exit
12.0ms	43×	body	640	valid
7.0ms	125×	body	80	valid
7.0ms	4×	body	2560	valid
3.0ms	21×	body	320	valid
3.0ms	81×	body	80	nan
2.0ms	9×	body	640	nan
2.0ms	16×	body	160	valid
1.0ms	8×	body	320	nan
1.0ms	3×	body	1280	nan
0.0ms	3×	body	160	nan

simplify221.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7

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: 25.0b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.2b	(log (+ (- 1.0 y) (* y (exp z))))
2.9b	(+ (- 1.0 y) (* y (exp z)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

5.0ms	(* y (exp z))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
13.0ms	(+ (- 1.0 y) (* y (exp z)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
163.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
75.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune344.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Merged error: 3.6b

Counts

115 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* z y) t)
5.3b	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
5.9b	(/ (* (pow z 2) y) t)
9.3b	(* (pow z 2) y)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
7×	`prod-exp`
6×	`times-frac` `div-exp` `associate-/r*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `associate-/l*` `unpow2` `sqr-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 87

Calls

4 calls:

4.0ms	(/ (* z y) t)
1.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
5.0ms	(/ (* (pow z 2) y) t)
5.0ms	(* (pow z 2) y)

series192.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (* z y) t)
118.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
28.0ms	(/ (* (pow z 2) y) t)
27.0ms	(* (pow z 2) y)

simplify44.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	300	473
1	1353	406
2	5002	406

prune336.0ms

Filtered

99 candidates to 68 candidates (68.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 3.0b

Counts

104 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (* z y) (/ 1 t))
5.3b	(fma (* (* z y) (/ 1 t)) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
5.9b	(/ (* (pow z 2) y) t)
9.3b	(* (pow z 2) y)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`add-sqr-sqrt`
18×	`prod-exp`
16×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
12×	`times-frac`
9×	`pow1` `associate-l`
8×	`div-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r*`
2×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `*-commutative` `div-inv` `unpow2` `sqr-pow`
1×	`frac-2neg` `associate-r/` `clear-num` `un-div-inv` `fma-udef` `associate-/l`

Counts

4 → 104

Calls

4 calls:

8.0ms	(* (* z y) (/ 1 t))
1.0ms	(fma (* (* z y) (/ 1 t)) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
6.0ms	(/ (* (pow z 2) y) t)
9.0ms	(* (pow z 2) y)

series149.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* z y) (/ 1 t))
94.0ms	(fma (* (* z y) (/ 1 t)) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
18.0ms	(/ (* (pow z 2) y) t)
18.0ms	(* (pow z 2) y)

simplify66.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	447	586
1	2338	487
2	5001	473

prune369.0ms

Filtered

116 candidates to 73 candidates (62.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	117	8	125

Merged error: 3.0b

Counts

125 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

9.3b	(* (pow z 2) y)
20.2b	(cbrt (/ (* z y) t))
20.2b	(cbrt (/ (* z y) t))
20.2b	(cbrt (/ (* z y) t))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
19×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `times-frac`
8×	`associate-l`
6×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-div` `pow1/3` `associate-r` `prod-exp` `div-inv`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

5.0ms	(* (pow z 2) y)
3.0ms	(cbrt (/ (* z y) t))
3.0ms	(cbrt (/ (* z y) t))
3.0ms	(cbrt (/ (* z y) t))

series270.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (pow z 2) y)
84.0ms	(cbrt (/ (* z y) t))
84.0ms	(cbrt (/ (* z y) t))
84.0ms	(cbrt (/ (* z y) t))

simplify117.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	203	483
1	591	448
2	3265	433
3	5002	406

prune397.0ms

Filtered

95 candidates to 72 candidates (75.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Merged error: 3.0b

Counts

103 → 8

regimes437.0ms

Accuracy

71.1% (4.9b remaining)

Error of 8.8b against oracle of 3.9b and baseline of 20.8b

bsearch76.0ms

Steps

Iters	Range		Point
8	-1.7954512872228914e-13	-2.0554488211069025e-17	-7.245223885126e-14

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	36
1	45	36

end0.0ms

sample3.1s

Algorithm

intervals

Results

790.0ms	1471×	body	1280	valid
740.0ms	1489×	body	10240	exit
447.0ms	1540×	body	640	valid
213.0ms	3570×	body	80	valid
165.0ms	902×	body	320	valid
99.0ms	77×	body	2560	valid
96.0ms	2602×	body	80	nan
52.0ms	470×	body	160	valid
51.0ms	258×	body	640	nan
37.0ms	119×	body	1280	nan
27.0ms	187×	body	320	nan
8.0ms	97×	body	160	nan